To answer this question, we need to consider what is meant by “the angle between 3 and 4”. Typically, when we refer to angles, we are talking about the degree of rotation between two lines or rays that share a common endpoint. For example, we might say that the angle between two intersecting lines is 90 degrees, or that the angle between two parallel lines is 0 degrees.
However, in this case, we only have two numbers – 3 and 4 – and no lines or rays to compare them to. So, it’s not clear how we would measure the angle between them. One possibility is that we are looking for the angle made by the numbers on a number line, where 3 and 4 are adjacent integers. In this case, we could say that the angle between 3 and 4 is 180 degrees, since they are on opposite sides of the number line and form a straight line.
Another possibility is that the question is asking for the angle between two vectors in a two-dimensional space, where 3 and 4 represent the components of the vectors. In this case, we would need more information about the orientation of the vectors to calculate the angle between them. Specifically, we would need to know the angle that each vector makes with a fixed axis (such as the x-axis), and then use the dot product formula to find the cosine of the angle between them.
Without more context or information, it’s difficult to determine exactly what is meant by “the angle between 3 and 4”. However, in general, when dealing with angles it is important to be clear about the reference lines, points or objects being compared, as it can greatly affect the value or interpretation of the angle.
What time is between 3 and 4 hands of a clock?
The position of the hands on a clock can represent a specific time. The hour hand moves incrementally as time passes and takes 12 hours to complete a full rotation, while the minute hand moves at a faster rate and takes 60 minutes to complete one full rotation. Therefore, at any given point in time, the hands of the clock are positioned at a particular angle relative to each other, representing the current time.
In this case, we are asked what time is between 3 and 4 hands of a clock. To answer this question, we first need to clarify which hands are being referred to. Based on the context of the question, it is safe to assume that the question is referring to the positions of the hour hand and the minute hand on a clock face.
Therefore, we can assume that the minute hand is pointing directly at the number 12, while the hour hand is positioned somewhere between the numbers 3 and 4.
To determine the precise time, we need to consider the angle between the two hands. At the top of the hour (i.e., when the minute hand is pointing at 12), the hour hand will be pointing directly at the number that corresponds to the current hour. As time passes, the hour hand will move slowly towards the next hour, while the minute hand will continue to move around the clock face.
At some point between 3 and 4 o’clock, the hour hand will be pointing at a position that is exactly halfway between the numbers 3 and 4. This corresponds to an angle of 90 degrees from the 12 o’clock position. At this same moment, the minute hand will have completed 1/4 of a full rotation, or 15 minutes.
Therefore, the time between 3 and 4 hands of a clock is 3:15.
The time between 3 and 4 hands of a clock is 3:15. This is determined by the angle between the hour hand and the minute hand, which is 90 degrees at the halfway point between 3 and 4, and by the fact that the minute hand has completed 1/4 of a full rotation at this time.
At what time between 3 and 4 the hand makes an angle of 10 degrees?
To answer this question, we need to know what type of clock is being referred to. Assuming that it is a standard 12-hour clock with an hour hand and a minute hand, we can use the following formula to determine at what time between 3 and 4 the hour hand makes an angle of 10 degrees:
Let x be the number of minutes past the hour that the hour hand is pointing to. Then, the minute hand will be pointing to 12x minutes past the hour. The angle between the hour hand and the minute hand is given by:
|30H – 11/2M|
where H is the hour and M is the number of minutes past the hour. The absolute value is necessary because the angle can be obtuse or acute, depending on the positions of the hands.
Since we know that the angle between the hands is 10 degrees, we can set up the equation:
|30(3) + 1/2x – 11/2(12x)| = 10
Simplifying this equation yields:
|90 + x/2 – 66x| = 20
Next, we need to solve for x. Since the absolute value term can be positive or negative, we need to consider two cases.
Case 1: 90 + x/2 – 66x = 20
Solving for x in this case yields:
x = 70/65 = 1.07692
Since x represents the number of minutes past the hour, we convert this to seconds:
1.07692 minutes * 60 seconds/minute ≈ 64.6 seconds
Therefore, the hour hand makes an angle of 10 degrees at approximately 3:01:04.6.
Case 2: 90 + x/2 – 66x = -20
Solving for x in this case yields:
x = 170/65 ≈ 2.61538
Converting this to seconds yields:
2.61538 minutes * 60 seconds/minute ≈ 156.92 seconds
Therefore, the hour hand makes an angle of 10 degrees at approximately 3:02:36.9.
There are two times between 3 and 4 at which the hour hand makes an angle of 10 degrees: 3:01:04.6 and 3:02:36.9.
At what time between 3 and 4 right angle is formed?
The question is asking at what time between 3 and 4 o’clock would a right angle be formed. In order to answer this question, we need to understand what a right angle is and how it is related to time.
A right angle is an angle that measures exactly 90 degrees. We use degrees to measure angles in geometry. Similarly, we use a 360-degree circle to measure time around the clock. Each hour on the clock represents 30 degrees of the full circle. Therefore, an hour hand pointing to a number on the clock would make an angle of 30 degrees to the horizontal.
To find the time at which a right angle is formed, we need to look for two points on the clock that are 90 degrees apart. Let’s start with 3 o’clock. The hour hand pointing to 3 makes an angle of 90 degrees to the horizontal, but this is not a right angle. We need to add some minutes to the hour hand to create a right angle.
To calculate how many minutes to add, we can use the fact that each minute on the clock advances the hour hand by half a degree. We need to add 90 – 30 = 60 degrees to the angle made by the hour hand at 3 o’clock. This means we need to add 120 minutes (2 hours) to the 3 o’clock position to form a right angle.
Therefore, the time at which a right angle is formed is 5 o’clock. At 5 o’clock, the hour hand and minute hand are 90 degrees apart, forming a right angle. This is because the hour hand would have advanced by 150 degrees (5 \* 30) from its starting position at 3 o’clock, and the minute hand would have advanced by 90 degrees from its starting position at 12 o’clock.
A right angle is formed at 5 o’clock on the clock. This is because the hour hand and minute hand are exactly 90 degrees apart, which satisfies the definition of a right angle.
What is the time between 3 and 4 when the angle between the hands of a watch is one third of a right angle?
To find the time between 3 and 4 when the angle between the hands of a watch is one third of a right angle, we need to use the formula:
Angle between the hands = |(11m – 60h) / 2| degrees
where h is the hours and m is the minutes.
First, let us find the angle between the hands when it is a right angle, which is 90 degrees. We can set up the equation:
90 = |(11m – 60h) / 2|
Since the absolute value of the equation is equal to 90, we can set up two cases, one for the positive value and one for the negative value:
(11m – 60h) / 2 = 90
11m – 60h = 180
and
-(11m – 60h) / 2 = 90
11m – 60h = -180
Now we need to find the values of h and m for each equation. Let’s start with the first one:
11m – 60h = 180
We know that the hour hand moves 30 degrees in one hour, and 60 degrees in two hours. Therefore, the angle between the hour hand and the 3 o’clock mark is:
3 * 30 = 90 degrees
We can set h = 3 and solve for m:
11m – 60(3) = 180
11m – 180 = 180
11m = 360
m = 32.73
Now we need to check if this value gives us an angle between the hands that is one third of a right angle:
Angle between the hands = |(11m – 60h) / 2|
= |(11(32.73) – 60(3)) / 2|
= |(360.03 – 180) / 2|
= 90.02
Since the angle is not exactly one third of a right angle, let’s try the other equation:
11m – 60h = -180
The angle between the hour hand and the 4 o’clock mark is:
4 * 30 = 120 degrees
We can set h = 4 and solve for m:
11m – 60(4) = -180
11m – 240 = -180
11m = 60
m = 5.45
Again, we need to check if this value gives us the desired angle between the hands:
Angle between the hands = |(11m – 60h) / 2|
= |(11(5.45) – 60(4)) / 2|
= |(-219.55) / 2|
= 109.78
This value is close to one third of a right angle, but not exactly. Therefore, there is no time between 3 and 4 when the angle between the hands is one third of a right angle.
At what time between 3 and 4 the angle between the minute hand and hour hand is 9?
To determine the time between 3 and 4 where the angle between the minute hand and hour hand is 9 degrees, we first need to understand how to calculate the angle between the two hands.
The hour hand moves at a slower pace than the minute hand. In one hour, the hour hand moves 30 degrees while the minute hand completes a full rotation of 360 degrees. Therefore, we can calculate the position of the hour hand as H = (hour * 30) + (minute * 0.5) and the position of the minute hand as M = minute * 6.
To determine the angle between the two hands, we subtract the position of the hour hand from the position of the minute hand and take the absolute value of the result. If the angle is greater than 180 degrees, we subtract the result from 360 to get the smallest angle between the two hands.
Using this formula, we can calculate the angle between the two hands for different times between 3 and 4.
At 3:00, the position of the hour hand is 90 degrees (3 * 30) and the position of the minute hand is also 90 degrees (3 * 6). The angle between the two hands is 0 degrees.
As time progresses, the position of the hour hand moves towards the next hour while the position of the minute hand constantly changes. At 3:15, the position of the hour hand is 97.5 degrees (3 * 30 + 15 * 0.5) and the position of the minute hand is 90 degrees (15 * 6). The angle between the two hands is 7.5 degrees.
At 3:30, the position of the hour hand is 105 degrees (3 * 30 + 30 * 0.5) and the position of the minute hand is 180 degrees (30 * 6). The angle between the two hands is 67.5 degrees.
As we approach 4:00, the angle between the two hands decreases. At 3:45, the position of the hour hand is 112.5 degrees (3 * 30 + 45 * 0.5) and the position of the minute hand is 270 degrees (45 * 6). The angle between the two hands is 157.5 degrees.
Finally, at some time between 3 and 4, the angle between the two hands is 9 degrees. Solving for this time requires some algebraic manipulation of the formula for the angle between the two hands.
| M – H | = | 6 * minute – (30 * hour + 0.5 * minute) |
Since we know that the angle between the two hands is 9 degrees, we can replace the absolute value with 9.
9 = | 6 * minute – (30 * hour + 0.5 * minute) |
Simplifying this equation, we get:
9 = | 5.5 * minute – 30 * hour |
We also know that the time must be between 3:00 and 4:00, so we can constrain the possible values for hour and minute.
3
0
Using this information, we can solve for the possible times where the angle between the two hands is 9 degrees. We can break this up into cases depending on whether the minute hand is ahead of the hour hand or vice versa.
Case 1: Minute hand ahead of hour hand
In this case, the minute hand is at a larger angle than the hour hand. From the equation above, we can see that this occurs when:
5.5 * minute – 30 * hour = 9
Solving for minute, we get:
minute = (30 * hour + 9) / 5.5
Since minute is a whole number, we can substitute in values for hour and see if we get a valid minute value.
If hour = 3, then minute = 27, which is a valid minute value since it is between 0 and 60.
If hour = 3.5, then minute = 30, which is not a valid minute value since it is equal to 60 (which is not allowed).
Therefore, the only solution in this case is that the time is 3:27.
Case 2: Hour hand ahead of minute hand
In this case, the hour hand is at a larger angle than the minute hand. From the equation above, we can see that this occurs when:
5.5 * minute – 30 * hour = -9
Solving for minute, we get:
minute = (30 * hour – 9) / 5.5
Since minute is a whole number, we can substitute in values for hour and see if we get a valid minute value.
If hour = 3, then minute = 15, which is a valid minute value since it is between 0 and 60.
If hour = 3.5, then minute = 12, which is not a valid minute value since it is negative.
Therefore, the only solution in this case is that the time is 3:15.
The time between 3 and 4 where the angle between the minute hand and hour hand is 9 degrees is either 3:15 or 3:27, depending on whether the minute hand is ahead of or behind the hour hand.
At what time between 3 o clock and 4 o clock will the minute hand and the hour hand are on the same straight line but in opposite direction?
To calculate the exact time when the minute hand and the hour hand will be on the same straight line but in opposite directions between 3 o’clock and 4 o’clock, we need to first understand the movement of the hour and minute hands.
The hour hand moves 30 degrees in one hour, or 0.5 degrees in one minute, while the minute hand moves 360 degrees in one hour or 6 degrees in one minute.
Now, let’s assume that at 3 o’clock, the hour hand makes an angle of 90 degrees with the 12 o’clock mark (this is because the hour hand is at the 3 o’clock mark), and the minute hand makes an angle of 180 degrees with the 12 o’clock mark (this is because the minute hand is pointing directly opposite to the 12 o’clock mark).
As time passes, the minute hand moves ahead while the hour hand remains at its position. For the minute hand to meet the hour hand in the opposite direction, it needs to cover a distance of 90 degrees (360 degrees – 270 degrees, which is the angle the hour hand has covered from 3 o’clock) while the hour hand remains at its position.
We can calculate this distance covered by the minute hand in terms of time by setting up an equation:
6t – 270 = 90
Where ‘t’ is the time in minutes after 3 o’clock.
Solving this equation, we get:
6t = 360
t = 60
Therefore, the minute hand will cover a distance of 90 degrees in 60 minutes, which means it will meet the hour hand in the opposite direction at 4 o’clock.
So, the exact time when the minute hand and the hour hand will be on the same straight line but in opposite direction is 4 o’clock.
What time does the clock show when the hour hand is between 3 and 4 and the angle between the two hands of the clock is 50 degree?
To solve this problem, we need to understand how the hour and minute hands move on a clock. The minute hand moves 360 degrees in 60 minutes, which means it moves 6 degrees every minute. The hour hand moves 360 degrees in 12 hours, which means it moves 30 degrees every hour, or 0.5 degrees every minute.
When the hour hand is between 3 and 4, we know it has moved past the 3 o’clock mark, but it has not yet reached the 4 o’clock mark. This means it has traveled a distance of 3 hours, or 90 degrees (since there are 360 degrees in a circle and the hour hand moves 30 degrees every hour).
To find the position of the minute hand, we need to determine how many minutes have passed since the last hour. If the hour hand is at the 3 o’clock position, we know that 15 minutes have passed (since each hour equals 60 minutes and we are one quarter of the way through the hour). If the hour hand has moved past the 3 o’clock mark, we need to calculate how many minutes have passed beyond the 15-minute mark.
To calculate the position of the minute hand, we can use the formula:
Position of Minute Hand = (Minutes Passed x 6) degrees
In this case, we know that the angle between the two hands is 50 degrees. We can use this information to set up an equation:
Position of Hour Hand – Position of Minute Hand = 50 degrees
Substituting in the values we know, we get:
90 – (Minutes Passed x 0.5) – (Minutes Passed x 6) = 50
Simplifying this equation, we get:
90 – 6.5 x Minutes Passed = 50
Subtracting 90 from both sides, we get:
-6.5 x Minutes Passed = -40
Dividing both sides by -6.5, we get:
Minutes Passed = 6.15
Since we cannot have a fraction of a minute on a clock, we can round this value to the nearest whole number, which is 6. This means that the minute hand has traveled 6 minutes past the 15-minute mark since the hour hand passed the 3 o’clock position.
Now, we can use the formula for the position of the minute hand:
Position of Minute Hand = (Minutes Passed x 6) degrees
Substituting in the value we just found, we get:
Position of Minute Hand = (6 x 6) degrees
Position of Minute Hand = 36 degrees
Therefore, the minute hand is at the 6-minute mark, which is 36 degrees past 12 o’clock. To find the exact time, we need to add this value to the angle that the hour hand is already at:
90 degrees (position of hour hand) + 36 degrees (position of minute hand) = 126 degrees
Since the hour hand is between 3 and 4, we know that it is closer to the 3 o’clock mark than the 4 o’clock mark. Therefore, we need to subtract this value from 360 degrees to get the angle from 12 o’clock:
360 degrees – 126 degrees = 234 degrees
To convert this angle into a time, we need to determine how many hours and minutes it represents. We know that 360 degrees represents 12 hours, or 720 minutes, on a clock. To find the ratio of degrees to minutes, we can use the formula:
Ratio of Degrees to Minutes = 720 / 360 = 2
Therefore, for every 1 degree on a clock, there are 2 minutes. To find the time that corresponds to 234 degrees, we can use the formula:
Time = (Degrees x Ratio of Degrees to Minutes) / 60
Substituting in the value we found, we get:
Time = (234 x 2) / 60
Time = 7.8 hours
Since we are measuring time on a clock, we need to convert this value into a time that is between 1 o’clock and 12 o’clock. We can do this by subtracting 12 from the value and taking the remainder:
7.8 – 12 = -4.2
Taking the remainder of this value, we get:
-4.2 + 12 = 7.8
Therefore, the time that the clock shows when the hour hand is between 3 and 4 and the angle between the two hands of the clock is 50 degrees is 7:48 (rounded to the nearest minute).
Is 3 4 and 5 a right angle?
Yes, 3, 4, and 5 can form a right angle. These three numbers are called Pythagorean triplets, and they satisfy the Pythagorean theorem, which states that the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse. In this case, if we consider 3 and 4 as the two shorter sides of the triangle, then the hypotenuse can be calculated as follows:
hypotenuse = √(3² + 4²)
= √(9 + 16)
= √25
= 5
Thus, we see that the hypotenuse of the triangle is equal to 5, which is also one of the numbers in the Pythagorean triplet. Hence, the triangle with sides 3, 4, and 5 forms a right angle and is a Pythagorean triplet. Additionally, because the sum of the squares of the two shorter sides (3² + 4²) equals the square of the hypotenuse (5²), this confirms that it is a right triangle.
Therefore, 3, 4, and 5 form a right angle in a right triangle.
What is the measure of 3 by 4 of a right angle?
To answer this question, it is important to first understand what a right angle is. A right angle is an angle that measures exactly 90 degrees. It is formed when two lines intersect perpendicularly, and is often symbolized by a square in geometric notation.
Now, if we are asked to find the measure of 3 by 4 of a right angle, it is likely that we are being asked to determine a portion or fraction of the 90-degree angle. To do this, we can use trigonometry, which is a branch of mathematics that deals with relationships between sides and angles of triangles.
Specifically, we can use the trigonometric ratios of the sides of a right triangle – namely, sine, cosine, and tangent – to find the desired measurement. Let’s assume that we are dealing with a right triangle that has a hypotenuse of length 1 (which means that its legs are 3/5 and 4/5, respectively, based on the Pythagorean Theorem).
If we want to find the sine of the angle corresponding to the 3/5 leg, we can write:
sin(theta) = opposite/hypotenuse
sin(theta) = (3/5)/1
sin(theta) = 0.6
This means that the angle whose opposite side is 3/5 of the hypotenuse has a sine of 0.6. We can also find the cosine and tangent of that angle using similar calculations:
cos(theta) = adjacent/hypotenuse
cos(theta) = (4/5)/1
cos(theta) = 0.8
tan(theta) = opposite/adjacent
tan(theta) = (3/5)/(4/5)
tan(theta) = 0.75
Now, it is unclear from the original question which of these trigonometric ratios is being referred to as “3 by 4” of the right angle. However, we can assume that it is likely one of these ratios, since they are commonly used in geometry and trigonometry. If we take “3 by 4” to refer to the sine of the angle, then we can say that “3 by 4 of a right angle” is equivalent to 0.6 times 90 degrees, or:
(3/4) * 90 = 67.5 degrees
Similarly, if we take “3 by 4” to refer to the cosine of the angle, we can say that the measurement is:
cos^-1(3/4) * 90 = 41.4 degrees
And if we take “3 by 4” to refer to the tangent of the angle, we can say that the measurement is:
tan^-1(3/4) * 90 = 36.9 degrees
All of these values represent a portion or fraction of the full 90-degree right angle, and would be useful in various geometric or trigonometric applications. However, without more specific information about what “3 by 4” refers to in this context, it is difficult to provide a definitive answer.
At what time between 3 and 4 the hands of a clock will considered with each other and point in the opposite direction respectively?
To solve this problem, we need to visualize a clock and understand how the hour and minute hands move. The hour hand moves at a slower pace than the minute hand, completing a full rotation every 12 hours. The minute hand rotates faster, completing a full rotation every hour.
Now, we are given a time frame between 3 and 4, which means that the hour hand will be somewhere between 3 and 4, while the minute hand will be on the 12 o’clock position. We need to find the exact time when the two hands are pointing in opposite directions.
To do this, we can use the formula:
Angle = (30 x Hour) – (11/2 x Minute)
This formula calculates the angle between the hour and minute hands. We know that when the two hands are pointing in opposite directions, the angle between them is 180 degrees. So, we can set the equation to find when the angle is equal to 180.
180 = (30 x Hour) – (11/2 x Minute)
Now, we need to plug in the values for our time frame. We know that the hour hand is somewhere between 3 and 4, so let’s start with Hour = 3. The minute hand is on the 12 o’clock position, so Minute = 0.
180 = (30 x 3) – (11/2 x 0)
Simplifying the equation:
180 = 90
This is not a possible solution, which means Hour = 3 is not the correct time. Let’s try Hour = 3.5, since this is the midpoint between 3 and 4.
180 = (30 x 3.5) – (11/2 x 0)
Simplifying the equation:
180 = 105
This is still not a possible solution. We can conclude that as the hour hand moves closer to 4, the angle between the hour and minute hands decreases. Therefore, we need to try a time that is closer to 4.
Let’s try Hour = 3.75.
180 = (30 x 3.75) – (11/2 x 0)
Simplifying the equation:
180 = 112.5
This is also not a possible solution. We need to keep trying until we get a valid solution.
Let’s try Hour = 3.9.
180 = (30 x 3.9) – (11/2 x 0)
Simplifying the equation:
180 = 117
This is a possible solution! When the hour hand is at 3.9 and the minute hand is on the 12 o’clock position, the two hands will point in opposite directions.
To find the exact minute at this time, we can calculate the angle between the minute hand and the 12 o’clock position. We know that the minute hand completes a full rotation every hour, so we can use the formula:
Angle = (6 x Minute)
We want to find when the angle between the minute hand and the 12 o’clock position is also 117 degrees.
117 = (6 x Minute)
Simplifying the equation:
Minute = 19.5
This means that at 3:19.5 (or approximately 3:20), the hands of the clock will be pointing in opposite directions.
The hands of a clock will point in opposite directions at approximately 3:20 when the hour hand is between 3 and 4. We determined this by using the formula to calculate the angle between the hour and minute hands, and finding the time when this angle was equal to 180 degrees.
At what time between 3 to 4 o clock will the hands of a clock make an angle which is exactly between 0 to 90?
To solve this problem, we need to use a bit of geometry and some basic knowledge about clocks. First, let’s understand what the question is asking. The hands of a clock consist of the hour hand and the minute hand. Between 3 to 4 o’clock, the hour hand will be pointing towards the 3 and the minute hand will be pointing towards the 12.
The question is asking us to find a time when the angle between the hour and minute hands is exactly between 0 and 90 degrees.
Let’s start by understanding how to calculate the angle between the hour and minute hands of a clock. We know that in 12 hours, the hour hand covers 360 degrees and the minute hand covers 720 degrees (because it moves twice as fast as the hour hand). This means that in one minute, the hour hand moves 0.5 degrees (360/12/60) and the minute hand moves 6 degrees (720/60).
Now, let’s assume that the time we are looking for is x minutes past 3 o’clock. At 3 o’clock, the hour hand is pointing directly at 3 and the minute hand is pointing at 12. After x minutes, the hour hand will move x * 0.5 degrees and the minute hand will move x * 6 degrees. The angle between the hour and minute hands can be calculated using the formula:
|0.5x – 6x/12| = |0.5x – 3x|
Simplifying this equation, we get:
|5.5x/12| = |1.5x|
At this point, we can solve for x by considering two cases: one where the hour hand is ahead of the minute hand, and one where the minute hand is ahead of the hour hand.
Case 1: Hour hand ahead of minute hand
If the hour hand is ahead of the minute hand, then the angle between the hands is the difference between their positions. This means that:
0.5x – 3x
-2.5x
x > 0
We can ignore the absolute value signs in this case. Solving the inequality, we get x > 0. This means that the time we are looking for occurs after 3 o’clock.
Case 2: Minute hand ahead of hour hand
If the minute hand is ahead of the hour hand, then the angle between the hands is the sum of their positions. This means that:
0.5x – 3x > 0
-2.5x > 0
x
Again, we can ignore the absolute value signs in this case. Solving the inequality, we get x
Putting the two cases together, we can conclude that the time we are looking for is between 3 o’clock and the first time when the minute hand overtakes the hour hand. This occurs when the minute hand has moved 30 minutes (because it moves at a rate of 6 degrees per minute and 30 * 6 = 180 degrees).
Therefore, the time we are looking for occurs sometime between 3 o’clock and 3:30.
To narrow down the time further, we need to find the exact value of x that satisfies the equation |5.5x/12| = |1.5x|. We can do this by considering two sub-cases.
Sub-case 1: 5.5x/12 = 1.5x
In this case, we get:
5.5x = 18x/12
66x = 216x
x = 0
However, this value of x does not satisfy our condition that the time should be between 3 o’clock and 3:30, so we can discard it.
Sub-case 2: 5.5x/12 = -1.5x
In this case, we get:
5.5x = -18x/12
66x = -216x
x = -3.27
This value of x corresponds to a time of approximately 3:18, which is the exact time when the angle between the hour and minute hands is 45 degrees.
Therefore, the answer to the question is that the hands of the clock make an angle which is exactly between 0 to 90 degrees at 3:18.
At what time the hands coincide?
The time at which the hands of a clock coincide depends on the type of clock and the position of the hands before they start moving.
In a standard analog clock, the hands coincide twice in a day – once during the early morning hours and once during the late afternoon or early evening hours. The exact time at which the hands coincide depends on the length of the hour and minute hands and the size of the clock face.
Assuming a clock with standard hour and minute hands and a circular clock face, the hands will coincide precisely at 12 o’clock, when both hands are pointing straight up towards the 12 on the clock face. They will also coincide precisely at 6 o’clock, when both hands are pointing straight down towards the 6 on the clock face.
Between these two points, the hands will approach each other and then move apart, until they reach their farthest distance apart at 6 o’clock. From there, they will start approaching each other again, until they coincide once more at 12 o’clock.
The time at which the hands coincide can also be impacted by the starting position of the hands. For example, if the minute hand is slightly ahead of the hour hand when the clock is started, it will take longer for the hands to coincide. Conversely, if the minute hand is slightly behind the hour hand, the hands will coincide sooner than usual.
The time at which the hands of a clock coincide can vary, but is typically either 12 o’clock or 6 o’clock, with the exact time depending on the size and type of the clock, as well as the starting position of the hands.