Question

question
an electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 34 feet up. the ladder makes an angle of 63° with the ground. find the length of the ladder. round your answer to the nearest tenth of a foot if necessary.

Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle where the height (opposite side to the given angle) is \(h = 34\) feet and the length of the ladder is the hypotenuse \(l\). The angle with the ground is \(\theta=63^{\circ}\). Using the sine function \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), so \(\sin(63^{\circ})=\frac{34}{l}\).

Step2: Solve for \(l\)

Rearrange the formula for \(l\): \(l=\frac{34}{\sin(63^{\circ})}\).
We know that \(\sin(63^{\circ})\approx0.891\). Then \(l=\frac{34}{0.891}\approx38.2\)

Answer:

The length of the ladder is approximately \(38.2\) feet.