pre calc

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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 hand at 11:40 p.m.
if you work it out this will help alot

• pre calc -

The hard part is finding the angle between the two hands.
Each hour represents 30°
so 11:40 = 11 2/3 hrs of rotation
the hour had is at the 350° position and the minute hand is at the 240° position,
so the angle between the two hands is 350-240 = 110°
now use the cosine law:
x^2= 5^2 + 6^2 - 2(5)(6)cos 110°
= 61 - 60cos110
= 81.5212
x = √81.5212 = 9.03 inches.

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