Question

an electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 31 feet up. the ladder makes an angle of 71° 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 the sine function, since $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 71^\circ$, opposite side $= 31$ ft, hypotenuse $= x$ (ladder length).
$\sin(71^\circ) = \frac{31}{x}$

Step2: Rearrange to solve for x

Isolate $x$ by cross-multiplying.
$x = \frac{31}{\sin(71^\circ)}$

Step3: Calculate the value

Use $\sin(71^\circ) \approx 0.9455$ to compute $x$.
$x \approx \frac{31}{0.9455} \approx 32.8$

Answer:

32.8 feet