Question

a surveyor 50 feet away from a building measures the angle from the ground to the top of the building to be 64°. what is the height of the building? ? feet. round your answer to the nearest hundredth.

Explanation:

Step1: Set up right - triangle relationship

We have a right - triangle where the adjacent side to the angle of elevation is 50 feet and we want to find the opposite side (height of the building). We use the tangent function: $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.
Let $h$ be the height of the building. The angle $\theta = 64^{\circ}$ and the adjacent side $x = 50$ feet. So, $\tan(64^{\circ})=\frac{h}{50}$.

Step2: Solve for height $h$

We know that $\tan(64^{\circ})\approx2.0503$. Then, $h = 50\times\tan(64^{\circ})$.
$h=50\times2.0503 = 102.515$ feet.

Answer:

$102.52$ feet