Posted by **jim** on Thursday, December 8, 2011 at 5:05pm.

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.

please help i don't understand how to do this.

if you work it out this will help alot

- pre calc -
**Reiny**, Thursday, December 8, 2011 at 5:36pm
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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