Question

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?

Short answer

So the distance is 137.3739 feet.

Step-by-step solution

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°.

Solution

We can draw a figure as: -

In $△ABC$we have to find $BC.$

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

$$\begin{gathered} \tan \left(c\right)\times BC=AB \\ \tan (20°)\times BC=50 \\ BC=\frac{50}{\tan (20°)} \\ BC=\frac{50}{0.3639} \\ BC\approx 137.3739 \end{gathered}$$

Final Answer

The distance is 137.3739 feet.