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Q. 54

Expert-verified
Found in: Page 517

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# 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?

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

See the step by step solution

## Step 1 Given Information

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

## Step 2 Solution

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

We can draw a figure as: -

In $△ABC$ we have to find $BC=x.$

$\mathrm{cos}\left(B\right)=\frac{BC}{AB}\phantom{\rule{0ex}{0ex}}BC=AB×\mathrm{cos}\left(B\right)\phantom{\rule{0ex}{0ex}}x=22×\mathrm{cos}\left(70\right)\phantom{\rule{0ex}{0ex}}x=22×0.342020\phantom{\rule{0ex}{0ex}}x=7.5244$

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