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 74° 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

Explanation:

Step1: Set up trigonometric relation

We have a right - triangle where the height (opposite side to the angle) is 33 feet and the angle between the ladder (hypotenuse) and the ground is 74°. We use the sine function $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Let the length of the ladder be $l$. So, $\sin(74^{\circ})=\frac{33}{l}$.

Step2: Solve for $l$

We can re - arrange the equation $\sin(74^{\circ})=\frac{33}{l}$ to $l = \frac{33}{\sin(74^{\circ})}$. Since $\sin(74^{\circ})\approx0.9613$, then $l=\frac{33}{0.9613}\approx34.3$.

Answer:

34.3 feet