Question

Use the following information to find the angle between the hands of a clock at 5:15.

Each hour, the hour hand of a clock moves This is 'th of the way around the circle. This is · 360° = 30°.
Each minute, the hour hand moves This is 'th of the distance it moves in one hour. This is · 30° = 0.5°
Each minute, the minute hand moves 'th of the way around the circle. This is · 360° = 6°.

Use the following information to find the angle between the hands of a clock at 5:15.

Each hour, the hour hand of a clock moves This is 'th of the way around the circle. This is · 360° =

Answer 1

I'll use the word interval to refer to the spacing between one number and a number adjacent to it on a clock. 12 of these in a clock and 360 degrees in a circle (clocks are circular), so each interval is 360/12 = 30 degrees.

If it's 15 minutes past five, the hand is at 5 and then a quarter of the way to 6. 5 and a quarter intervals = 30 * 5.25 = 157.5 degrees.

If the minute hand has gone for 15 minutes, it's at the 3. That's 3 intervals, so: 3 * 30 = 90. We want the distance between those two which is just the difference.

157.5 - 90 = 67.5