Question

The minute hand of a clock is 12 cm long, and the hour hand is 10cm long. Determine the distance between the tips of the hands at 9:30pm, to the nearest mm.

Answer 1

At 12:00 the hands are together
After h hours, the hour hand has gone h/12 * 360 degrees
After m minutes, minute hand has gone m/60 * 360 degrees
9:30 = 9.5 hours
:30 = 30 minutes
So, the hour hand has gone 9.5/12*360 = 285° and the minute hand is at 180°

So, the angle between the hands is 105°

Finally, the distance d between the tips is

d^2 = 12^2 + 10^2 - 2*10*12 cos105°