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Solution

The traffic light system is in equilibrium, so we know that the net torque and force must be zero. Since we don't know what role the wall plays in the system, we'll place the pivot point there and concentrate on the torques.

The unknown angle value can be discovered by using the torque formula. We know that the vertical force that the tension supplies can be found using the equation:

SinA = Fy/5000 N
SinA (5000 N) = Fy
This value can be inserted into the torque formula where A (or the angle value) can be solved for.

Torque CW = Torque CCW
(4.5 m)(490 N) + (19.6 N)(2.25 m) = (5000 N)(SinA)
(5000 N)(SinA) = 2249.1 N*m
A = 27 degrees