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: Identify trigonometric relationship

We have a right triangle where the opposite side to the angle \(68^\circ\) is 32 feet (height on the wall), and the ladder is the hypotenuse (\(x\)). We use the sine function: \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\). So \(\sin(68^\circ)=\frac{32}{x}\).

Step2: Solve for \(x\)

Rearrange the formula: \(x = \frac{32}{\sin(68^\circ)}\). Calculate \(\sin(68^\circ)\approx0.9272\). Then \(x=\frac{32}{0.9272}\approx34.5\).

Answer:

The length of the ladder is approximately 34.5 feet.