Question

suppose that you are headed toward a plateau 62.1 meters high. if the angle of elevation to the top of the plateau is 39.5°, how far are you from the base of the plateau? what is your distance from the base of the plateau? meters (round to one decimal place as needed.)

Explanation:

Step1: Recall tangent formula

We know that $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$ in a right - triangle. Here, the height of the plateau is the opposite side ($h = 62.1$ meters) and the distance from the base of the plateau is the adjacent side ($d$), and $\theta=39.5^{\circ}$. So, $\tan\theta=\tan(39.5^{\circ})=\frac{h}{d}$.

Step2: Solve for $d$

We can re - arrange the formula $\tan(39.5^{\circ})=\frac{62.1}{d}$ to get $d=\frac{62.1}{\tan(39.5^{\circ})}$.
We know that $\tan(39.5^{\circ})\approx0.829$. Then $d=\frac{62.1}{0.829}\approx74.9$.

Answer:

$74.9$