# Suppose that you are headed toward a plateau 50 meters high. If the angle of elevation to the top of the plateau is 60°, how far are you from the base

Suppose that you are headed toward a plateau 50 meters high. If the angle of elevation to the top of the plateau is $$60^{\circ}$$, how far are you from the base of the plateau?

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berggansS

Let x be the distance from the base of the plateau to you. Draw the situation as shown: [Triangle]
Since x is the side adjacent the $$60^{\circ}$$ angle and we are given the length of the side opposite the angle, then we can use the tangent ratio to write: $$\displaystyle{\tan{{60}}}°={o}{p}\frac{{p}}{{a}}{d}{j}=\frac{{50}}{{x}}$$
$$\displaystyle{x}=\frac{{50}}{{\tan{{60}}}}°$$
Use a calculator in DEGREE mode $$x \sim 28.9m$$

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content_user

Answer is given below (on video)