Question

suppose that you are headed toward a plateau 32.5 meters high. if the angle of elevation to the top of the plateau is 18.5°, 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 ($y = 32.5$ meters) and the distance from the base of the plateau is the adjacent side ($x$), and $\theta = 18.5^{\circ}$. So, $\tan(18.5^{\circ})=\frac{32.5}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{32.5}{\tan(18.5^{\circ})}$. Since $\tan(18.5^{\circ})\approx0.337$, then $x=\frac{32.5}{0.337}\approx96.4$.

Answer:

$96.4$