What is the angle between the hour hand and minute hand of a clock if it shows 3:15?
Here is an image that displays the positions of the hour hand and minute hand on a clock at 3:15 for your reference.
Clock Angle Puzzle solution
To calculate the angle between the hour hand and minute hand on a clock at 3:15, we need to use the following formula:
angle = |(30 * H) – (11/2 * M)|
Where H is the hour in 24-hour format, and M is minute.
In this case, H = 3 and M = 15. Plugging these values into the formula, we get:
angle = |(30 * 3) – (11/2 * 15)| angle = |90 – 82.5| angle = 7.5 degrees
Therefore, the angle between the hour hand and minute hand on a clock at 3:15 is 7.5 degrees.
At a quarter past the hour, the minute hand is pointing to the 3, while the hour hand has moved 1/4 of the way from the 3 to the 4. This means that the hour hand is pointing to the 3 and 1/4 marks on the clock face. Since there are 12 marks on a clock, each representing 30 degrees (360 degrees/12 marks), 1/4 of a mark represents 30 degrees/4 or 7.5 degrees. Therefore, the angle between the hour hand and the minute hand of the clock is 7.5 degrees at 3:15.
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