Chapter 9.7, Problem 35E

To determine

To find the tension in the wires.

Answer to Problem 35E

The tension in the wires is $27.21$ pounds

Explanation of Solution

Given:

The wires form an ${130}^{\circ }$ angle with each other and the prop weighs $23$ pounds.

Calculation:

The diagram of the situation is as follows-

  

Now, using the law of sines to find the force exerted by the cables as follows-

  $\begin{array}{l}\frac{23}{\sin {50}^{\circ }}=\frac{x}{\sin {65}^{\circ }}\{\text{ base angle=}\frac{180-50}{2}={65}^{\circ }\}\\ x=\frac{23\sin {65}^{\circ }}{\sin {50}^{\circ }}\\ x=27.21\end{array}$

Therefore, the tension in the wires is $27.21$ pounds.