Puzzle – Degrees between Hand of Clocks on 3:15
Puzzle: What is the angle between the hour hand and the minute hand on a clock if the time is 3:15?
Solution:
This type of problem, to find the angle between the hour hand and the minute hand, can be solved using the following steps.
- Find the angle made by the minute hand with the 12 o’clock position.
- Find the angle made by the hour hand with the 12 o’clock position.
- Calculate the difference between these two angles, which is the angle between the hour hand and minute hand.
Step 1: Calculate the angles by considering the 12 O’clock position as a reference.
- Angle made by minute hand: minute hand completes one rotation in one hour i.e 60 minutes.
So in one minute, it moves by 360/60 = 6°. - Angle made by Hour hand: hour hand completes one rotation in 12 hours. i.e 720 minutes.
So it moves by 360/12 = 30° in one hour and 360/720 = 0.5° in one minute.
In H hours and M minutes, with respect to the 12 o’clock position the angle made by the minute hand = M×6° and the angle made by the hour hand = (H×30 + M×0.5)°.
Step 2 (degrees at 3:15):
At 3:15 in the clock, H = 3 and M = 15.
Angle made by minute hand = M×6° = 15×6° = 90°
Angle made by hour hand = (H×30 + M×0.5)° = (3×30 + 15×0.5) ° = 97.5°
Angle between hour hand and minute hand = 97.5° – 90° = 7.5°
The angle between the hour hand and the minute hand on a clock at 3:15 is 7.5°
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