posted by Sammy on .
If the length of the hour and the minute hands of a clock are 4 cm and 6 cm, respectively, what is the distance in cm between the tips of the hands at two o'clock?
there are 30° per hour
at 2:00, the minute hand is at 90°-60°=30° (measuring from horizontal)
the hour hand is at 90-(60+30/6) = 25°
minute tip is at (6cos30°,6sin30°) = (5.2,3.0)
hour tip is at (4cos25°,4sin25°)=(3.6,1.7)
d^2 = 1.6^2 + 1.3^2
d = 2.1 cm
oops I was thinking 2:10
at 2:00, the hands are at (0,6) and (3.46,2)
d = 5.3 cm