In this clock the minute hand is 14 cm long and the hour hand 7 cm. How far apart are the tips of the two hands at the time shown?

At 4:00 the angle between the hands is 120°. By the cosine rule, $d^2=14^2+7^2-2\times 14\times 7\times$ cos 120° = 196 + 49 + 98 = 343, so $d$ = √343 = 7√7 cm. (7√5 cm uses a right angle, as at 3:00; 21 cm adds the lengths as if the hands were opposite.)