SOLUTION: an electric hoist is being used to lift a beam. The diameter of the drum on the hoist is 8 in, and the beam must be raised 2.5 feet. Find the number of degrees through which the dr

Algebra ->  Trigonometry-basics -> SOLUTION: an electric hoist is being used to lift a beam. The diameter of the drum on the hoist is 8 in, and the beam must be raised 2.5 feet. Find the number of degrees through which the dr      Log On


   

Question 914148: an electric hoist is being used to lift a beam. The diameter of the drum on the hoist is 8 in, and the beam must be raised 2.5 feet. Find the number of degrees through which the drum must rotate. Round your answer to the nearest whole number.
a) 37 deg
b)36 deg
C) 39 deg
D) 38 deg
I have been trying at this equation for hours. I can not understand it at all.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The wire rides along the outside of the drum.
As the drum rotates the wire is pulled up and wraps around the drum, lifting the beam.
If the drum is rotated in the opposite direction, the wire would unwrap from the drum and the beam would lower.
If the drum was to make one revolution, the length of wire captured would be equal to the circumference of the circle (the drum).
Make up a ratio.
I think you have an error in your setup.
The drum diameter must be in feet and not inches or else the answer is not one of the given choices.
360%2FC=theta%2F2.5%29
For a circle,
C=2pi%2AR=pi%2AD=8pi
Substitute,
360%2F%288pi%29=theta%2F%282.5%29
theta=%28360%282.5%29%29%2F%288pi%29
theta=35.81
Rounding up,
theta=36degrees