If the two wires make the same angle with the vertical, the angle must be 83.6⁰.
What is the angle between the wires?
The angle between the two wires is determined by applying the principle of parallelogram law of vector addition.
R² = a² + b² - 2abcosθ
where;
- R is the resultant vector = weight of the frame = W
- a is tension in first wire = 0.75W
- b is the tension in the second wire = 0.75W
- θ is angle between the two wires
W² = (0.75W)² + (0.75W)² - 2(0.75W x 0.75W) cosθ
W² = 1.125W² - 1.125W² cosθ
W² = 1.125W²(1 - cosθ)
W²/1.125W² = 1 - cosθ
0.8889 = 1 - cosθ
cosθ = 1 - 0.8889
cos θ = 0.1111
θ = arc cos(0.1111)
θ = 83.6⁰
Thus, the angle between the two wires is determined as 83.6⁰.
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