Question

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 x-y 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 + (-4.33-4.924)^2)
= √(2.663 + 85.636)
= √88.3
= 9.4 in

Makes sense, since at 6:00 they'd be 11.0 inches apart.

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