Question

suppose that you are headed toward a plateau 60 m high. if the angle of elevation to the top of the plateau is 25°, how far are you from the base of the plateau?
the plateau is □ meters away.
(do not round until the final answer. then round to two decimal places as needed.)

Explanation:

Step1: Use the tangent function

In a right - triangle, if the height of the plateau (opposite side) is \(h = 60\) m and the distance from the base of the plateau (adjacent side) is \(x\), and the angle of elevation \(\theta=25^{\circ}\). The tangent function is defined as \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). So, \(\tan(25^{\circ})=\frac{60}{x}\).

Step2: Solve for \(x\)

We can rewrite the equation from Step 1 as \(x = \frac{60}{\tan(25^{\circ})}\).
We know that \(\tan(25^{\circ})\approx0.4663\). Then \(x=\frac{60}{0.4663}\approx128.67\)

Answer:

\(128.67\)