Question

suppose that you are headed toward a plateau 34.8 meters high. if the angle of elevation to the top of the plateau is 26.5°, 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 trigonometric relationship

We have a right triangle where the height of the plateau (opposite side to the angle of elevation) is \( 34.8 \) meters, the angle of elevation \( \theta = 26.5^\circ \), and we need to find the adjacent side (distance from the base, let's call it \( x \)). The tangent function relates the opposite and adjacent sides: \( \tan\theta=\frac{\text{opposite}}{\text{adjacent}} \), so \( \tan(26.5^\circ)=\frac{34.8}{x} \).

Step2: Solve for \( x \)

Rearrange the formula to solve for \( x \): \( x = \frac{34.8}{\tan(26.5^\circ)} \). Calculate \( \tan(26.5^\circ) \approx 0.5005 \). Then \( x=\frac{34.8}{0.5005}\approx 69.5 \).

Answer:

\( 69.5 \)