SOLUTION: A force of 365 lb is needed to hold a 500 lb piano on an incline. What angle does the incline make with the horizontal?

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Question 1116682: A force of 365 lb is needed to hold a 500 lb piano on an incline. What angle does the incline make with the horizontal?
Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
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Let "a" be the angle which the incline makes with the horizontal line.


Then, after decomposition the weight force along and perpendicularly to the incline you get for the force along the incline 

    
    F = W*sin(a).


Then F is exactly the force needed to hold the piano on the inline.


In your case, W and F are given, and you obtain for the angle "a"  sin(a) = F%2FW = 365%2F500 = 0.712.


It gives you  a = arcsin(0.712) = 0.792 radians = 45.4 degrees.

Solved.