1.81 Muscles and Bones: Vector Magnitude Problem

[cdlegendary]

Homework Statement

A patient in therapy has a forearm that weighs 23.0 N and that lifts a 114.0 N weight. These two forces have direction vertically downward. The only other significant forces on his forearm come from the biceps muscle (which acts perpendicularly to the forearm) and the force at the elbow. If the biceps produces a pull of 232 N when the forearm is raised 44 degrees above the horizontal, find the magnitude and direction of the force that the elbow exerts on the forearm. (The sum of the elbow force and the biceps force must balance the weight of the arm and the weight it is carrying, so their vector sum must be 137.0 N, upward.)

Homework Equations

So there's 3 vectors I think:
A: angle ?, magnitude -137N
B: angle 44 degrees, magnitude ?
C: angle 134 degrees, magnitude 232 N

The Attempt at a Solution

I don't think I have my question setup correctly, but I tried:

232sin(44) = 161.2N = x
232cos(44) = 166.9N = y

Then I use the law of cosines, but doesn't really work..if someone could walk me through the setup, I would greatly appreciate it.

 

[ideasrule]

First, draw a free-body diagram of the forearm. Label all forces, then write out Newton's second law for both the x and y directions.