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 70° with the ground. find the length of the ladder. round your answer to the nearest hundredth of a foot if necessary.

Explanation:

Step1: Use sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 70^{\circ}\), the opposite side to the angle \(\theta\) is \(24\) (height of the electric box) and the hypotenuse is \(x\) (length of the ladder). So, \(\sin70^{\circ}=\frac{24}{x}\).

Step2: Solve for \(x\)

We can rewrite the equation as \(x=\frac{24}{\sin70^{\circ}}\). Since \(\sin70^{\circ}\approx0.9397\), then \(x = \frac{24}{0.9397}\).

Step3: Calculate the value of \(x\)

\(x=\frac{24}{0.9397}\approx25.54\)

Answer:

The length of the ladder is approximately \(25.54\) feet.