Posted by jim 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 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,
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 350240 = 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.