Question

An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 31 feet up. The ladder makes an angle of 75∘ with the ground. Find the length of the ladder. Round your answer to the nearest hundredth of a foot if necessary.

Answer 1

Let us begin by picturing the problem using a diagram:

Using your trigonometric ratios, we can find the length of the ladder. I have labelled the length of the ladder as x

Let us identify the sides of the triangle:

Opposite side = 31 ft

Hypothenuse side = x

Using the sine ratio:

$\sin \text{ }\theta\text{ = }\frac{Opposite}{Hypothenuse}$$\begin{gathered} \sin 75^0\text{ = }\frac{31}{x} \\ \text{Cross}-\text{Multiply} \\ x\text{ }\times sin75^0\text{ = 31} \\ \text{Divide both sides by sin75}^0 \\ x\text{ = }\frac{31}{\sin 75^0} \\ =\text{ 32.09} \end{gathered}$

Hence, the length of the ladder is 32.09 feet

Answer: 32.09 feet