Question

A sign with a weight of 80N hangs from a vertical cable tied to 2 other cables. The upper cables make angles of 37 degrees and 53 degrees with the horizontal. Find the tension force in each cable.

Answer 1

Consider the tension in the first cable as T1 and the tension in the second cable as T2
Equating the horizontal forces,
T1 cos $\theta$ 1 = T2 cos $\theta$ 2
Where $\theta$ 1 and $\theta$ 2 are the angles 37 and 53 respectively.
T1 cos(37) = T2 cos(53)
T1 x 0.798 = T2 x 0.602
T1 = 0.754 T2          ...(1)

Equating the vertical forces,
T1 sin $\theta$ 1 + T2 sin $\theta$ 2 = 80
T1 x 0.612 + T2 x 0.798 = 80
Substituting T1,
0.754 T2 + 0.798 T2 = 80
T2 = 51.54 N

T1 = 0.754 T2
= 38.84 N