Question

an electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 29 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: Use the sine function

In a right - triangle (formed by the ladder, the ground, and the wall), the sine of an angle is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Let the length of the ladder be $L$ (hypotenuse), the height of the electric box (opposite side) $h = 29$ feet, and the angle $\theta=71^{\circ}$. So, $\sin(71^{\circ})=\frac{29}{L}$.

Step2: Solve for $L$

We can rewrite the equation from Step 1 as $L=\frac{29}{\sin(71^{\circ})}$.
We know that $\sin(71^{\circ})\approx0.9455$. Then $L=\frac{29}{0.9455}$.

Step3: Calculate the value of $L$

$L=\frac{29}{0.9455}\approx30.7$

Answer:

The length of the ladder is approximately $30.7$ feet.