Question

if the sun is 55° above the horizon, find the length of the shadow cast by a building 78 ft tall. round your answer to the nearest tenth.

Explanation:

Step1: Use trigonometric ratio

We know that in a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 55^{\circ}\), the opposite side is the height of the building (\(h = 78\) ft) and the adjacent side is the length of the shadow (\(x\)). So, \(\tan(55^{\circ})=\frac{78}{x}\).

Step2: Solve for \(x\)

We can rewrite the equation as \(x=\frac{78}{\tan(55^{\circ})}\). Since \(\tan(55^{\circ})\approx1.4281\), then \(x=\frac{78}{1.4281}\approx54.6\).

Answer:

\(54.6\) ft