Question

A clock is showing the time as exactly 3:00 p.m. and 25 s. Because a full minute has not passed since 3:00, the hour hand is pointing directly at the 12. If the tip of the second hand is directly below the tip of the hour hand, and if the length of the second hand is 9 cm, what is the length of the hour hand?

Answer 1

I had to read this a couple of times to see this was not about time, but is a right triangle problem. If the hour hand is at three, let us consider that a leg of a right triangle, we will consider the hypotenuse as the second hand.
Sketch the picture. 

The hypotenuse is 9 cm. the angle is found by: 

the (hour hand) is pointing directly at the 12. I expect you mean the minute hand. The angle between the minute hand and the second hand is 25/60*360 = 150 which make the angle between the hour hand and the second hand. 150 -90 =60 

so the second hand and the hour hand gives us a right triangle, with a 60 degree angle and a hyp. of 9 cm. 

cos 60 = x/9 

9 cos 60 =x 

x = 4.5 cm

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