Question

an electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 24 feet up. the ladder makes an angle of 73° with the ground. find the length of the ladder. round your answer to the nearest tenth of a foot if necessary. answer attempt 1 out of 2 feet submit answer

Explanation:

Step1: Use the sine function

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 73^{\circ}$, the opposite side to the angle $\theta$ is $24$ (height of the electric box) and the hypotenuse is the length of the ladder $x$. So, $\sin(73^{\circ})=\frac{24}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{24}{\sin(73^{\circ})}$.
We know that $\sin(73^{\circ})\approx0.9563$. Then $x=\frac{24}{0.9563}\approx25.1$.

Answer:

$25.1$