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Calculus III Question

A weight of 100 pounds is suspended by two ropes A and B. Rope A makes an angle of 30 degrees with the ceiling and rope B makes an angle of 45 degrees with the ceiling. What are the magnitudes of the forces in each of the ropes?
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1 Answer

This is not a calculus problem.  It is a problem in elementary statics.  Set up force equilibrium in the x and y directions, which will give you 2 equations in the 2 unknown forces, and then solve for the 2 forces.
x direction:
FAcos30° - FBcos45° = 0
y direction:
FAsin30° + FBsin45° = 100 lbs
Solve for FA and Fin
0.8660FA - 0.7071FB = 0
0.5FA + 0.7071FB = 100
You should get
FA = 73.21 lbs
FB = 89.66 lbs