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

Cem Hayes 2021-06-13 Answered

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
Answered 2021-06-14 Author has 23919 answers

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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Answered 2021-09-14 Author has 11052 answers

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