Question

an electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 33 feet up. the ladder makes an angle of 80° 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 ratio

We have a right triangle where the opposite side to the \(80^\circ\) angle is 33 feet (height on the wall), and the ladder is the hypotenuse (\(x\)). The sine function relates the opposite side and the hypotenuse: \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\). So, \(\sin(80^\circ)=\frac{33}{x}\).

Step2: Solve for \(x\)

Rearrange the formula to solve for \(x\): \(x = \frac{33}{\sin(80^\circ)}\). Calculate \(\sin(80^\circ)\approx0.9848\). Then \(x=\frac{33}{0.9848}\approx33.5\).

Answer:

The length of the ladder is approximately \(\boldsymbol{33.5}\) feet.