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 $80^\circ$ 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 use $\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}$, where $\theta=80^\circ$, opposite side $=33$ ft, hypotenuse $=x$ (ladder length).
$\sin(80^\circ) = \frac{33}{x}$

Step2: Rearrange to solve for $x$

Isolate $x$ by cross-multiplying.
$x = \frac{33}{\sin(80^\circ)}$

Step3: Calculate the value

Use $\sin(80^\circ)\approx0.9848$ to compute $x$.
$x \approx \frac{33}{0.9848} \approx 33.5$

Answer:

33.5 feet