Question

question
an electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 22 feet up. the ladder makes an angle of 77° with the ground. find the length of the ladder. round your answer to the nearest tenth of a foot if necessary.
answer attempt 1 out of 2
feet submit answer

Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle where the height (opposite side to the given angle) is \(h = 22\) feet and the angle with the ground \(\theta=77^{\circ}\), and we need to find the length of the ladder (hypotenuse \(L\)). Using the sine function \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), so \(\sin(77^{\circ})=\frac{22}{L}\).

Step2: Solve for \(L\)

Rearrange the formula to \(L=\frac{22}{\sin(77^{\circ})}\). We know that \(\sin(77^{\circ})\approx0.9744\). Then \(L=\frac{22}{0.9744}\approx22.6\).

Answer:

\(22.6\)