Question

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 relationship

The height (33 ft) is opposite the 80° angle; ladder length \(x\) is hypotenuse. Use \(\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}\).
$$\sin(80^\circ) = \frac{33}{x}$$

Step2: Solve for \(x\)

Rearrange to \(x = \frac{33}{\sin(80^\circ)}\).
$$x = \frac{33}{\sin(80^\circ)} \approx \frac{33}{0.9848} \approx 33.5$$

Answer:

33.5 feet