math
posted by bob on .
the hour hand of a clock is 5 inches long and the minute hand is 6 inches long. determine the distance between the tips of the hands at 11:40 pm????

at 11:40 pm the hour hand only has 1/36 of a complete revolution to go. That's 10 degrees
so, the tip of the hour hand is at
(5,pi/2+pi/18) in polar coordinates. That is
(.868,4.924) in xy coordinates
The tip of the minute hand is at
(6,2pi/3), or
(2.500,4.330)
so, the tips of the hands are
√((2.5+.868)^2 + (4.334.924)^2)
= √(2.663 + 85.636)
= √88.3
= 9.4 in
Makes sense, since at 6:00 they'd be 11.0 inches apart.