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.

The answer is 17.5 cm I need to work on how to get to that answer!
at 9:30 the hour hand has gone clockwise 9.5/12 * 360 = 285° from the top
The minute hand is at 180°

So, the angle between them is 105°. You want d where

d^2 = 12^2 + 10^2 - 2*12*10*cos 105°
d^2 = 306.1
d = 17.5

Just a straightforward application of the law of cosines.

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