Question

if the sun is 64° above the horizon, find the length of the shadow cast by a 98 - foot tall building. round your answer to the nearest tenth of a foot.

Explanation:

Step1: Define trigonometric relation

We use the tangent function: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$, where $\theta=64^\circ$, opposite side = 98 ft (building height), adjacent side = shadow length $x$.
Rearranged: $x = \frac{98}{\tan(64^\circ)}$

Step2: Calculate $\tan(64^\circ)$

$\tan(64^\circ) \approx 2.0503$

Step3: Compute shadow length

$x \approx \frac{98}{2.0503} \approx 47.8$

Answer:

47.8 feet