Question

A 22-foot extension ladder leaning against a building makes a 70° angle with the ground. How far up the building does the ladder touch?

Short answer

Hence, the ladder touch the building at $7.5244$feet.

Step-by-step solution

Given Information

Given that a 22-foot extension ladder leaning against a building makes a 70° angle with the ground.

Solution

Suppose the ladder touch the building at $x$feet.

We can draw a figure as: -

In $△ABC$we have to find $BC=x.$

$$\begin{gathered} \cos \left(B\right)=\frac{BC}{AB} \\ BC=AB\times \cos \left(B\right) \\ x=22\times \cos \left(70\right) \\ x=22\times 0.342020 \\ x=7.5244 \end{gathered}$$

Final answer

Hence, the ladder touch the building at$7.5244$feet.