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.

Explanation:

Step1: Identify the trigonometric relationship

We have a right triangle where the height on the wall (opposite side to the angle with the ground) is 33 feet, the ladder is the hypotenuse (let's call its length \( L \)), and the angle with the ground is \( 74^\circ \). We use the sine function, which is defined as \( \sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}} \). So, \( \sin(74^\circ)=\frac{33}{L} \).

Step2: Solve for \( L \)

Rearrange the formula to solve for \( L \): \( L = \frac{33}{\sin(74^\circ)} \). Calculate \( \sin(74^\circ) \approx 0.9613 \). Then, \( L=\frac{33}{0.9613}\approx 34.3 \).

Answer:

The length of the ladder is approximately 34.3 feet.