tension and vectors?

Question

A street lamp weighs 150 N . It is supported equally by two wires that form an angle of 106 degrees with each other. What is the tension of these wires in Newtons?

Answer 1

106/2 = 53°
2Tcos53° = 150
T = 75/cos53°
T = 124.623 N

Answer 2

cos (106/2) = (150/2)/h

rearange:

h = (150/2) / (cos (106/2))

or

h = 150 / (2*cos (106/2))

Essentially what you do is divide the force of the lamp by both wires: (150/2)

Then, setting the wire on each side as a hypotenuse (h) of a triangle, and (150/2) as the vertical member of both triangles because they each support half of the original force.

The angle between the vertical and the hypotenuse of each triangle is (106/2).

Then, using the angle (106/2), the hypotenuse (h) and the vertical members (150/2) you can calculate the cos of the angle (106/2) using cos (106/2).

This will give you ((150/2)/h)