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Q. 53

Expert-verified
Found in: Page 517

Precalculus Enhanced with Graphing Utilities

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

Suppose that you are headed toward a plateau 50 meters high. If the angle of elevation to the top of the plateau is 20°, how far are you from the base of the plateau?

So the distance is 137.3739 feet.

See the step by step solution

Step 1 Given Information

Suppose that you are headed toward a plateau 50 meters high. If the angle of elevation to the top of the plateau is 20°.

Step 2 Solution

We can draw a figure as: -

In $△ABC$ we have to find $BC.$

$\mathrm{tan}\left(C\right)=\frac{AB}{BC}$

$\mathrm{tan}\left(c\right)×BC=AB\phantom{\rule{0ex}{0ex}}\mathrm{tan}\left(20°\right)×BC=50\phantom{\rule{0ex}{0ex}}BC=\frac{50}{\mathrm{tan}\left(20°\right)}\phantom{\rule{0ex}{0ex}}BC=\frac{50}{0.3639}\phantom{\rule{0ex}{0ex}}BC\approx 137.3739$