Question

an electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 32 feet up. the ladder makes an angle of 68° with the ground. find the length of the ladder. round your answer to the nearest tenth of a foot if necessary.

Explanation:

Step1: Use the sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 68^{\circ}\), the opposite side to the angle \(\theta\) is \(32\) (height of the electric box) and the hypotenuse is \(x\) (length of the ladder). So, \(\sin(68^{\circ})=\frac{32}{x}\).

Step2: Solve for \(x\)

We can rewrite the equation as \(x=\frac{32}{\sin(68^{\circ})}\).
We know that \(\sin(68^{\circ})\approx0.9272\). Then \(x=\frac{32}{0.9272}\approx34.5\).

Answer:

The length of the ladder is approximately \(34.5\) feet.