Question

suppose that you are headed toward a plateau 24.8 meters high. if the angle of elevation to the top of the plateau is 17.5°, 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: Identify the trig - function

We have a right - triangle situation where the height of the plateau is the opposite side and the distance from the base is the adjacent side with respect to the angle of elevation. We use the tangent function $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.
Let the height of the plateau $h = 24.8$ meters, the angle of elevation $\theta=17.5^{\circ}$, and the distance from the base of the plateau be $x$. Then $\tan\theta=\tan(17.5^{\circ})=\frac{h}{x}$.

Step2: Solve for $x$

We can re - arrange the formula $\tan(17.5^{\circ})=\frac{24.8}{x}$ to get $x=\frac{24.8}{\tan(17.5^{\circ})}$.
We know that $\tan(17.5^{\circ})\approx0.316$.
So $x=\frac{24.8}{0.316}\approx78.5$.

Answer:

$78.5$