Question

the length of a shadow of a building is 58 ft when the sun is 57° above the horizon. find the height of the building. round your answer to the nearest tenth.

Explanation:

Step1: Use the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 57^{\circ}\), the adjacent side (length of the shadow) \(a = 58\) ft, and the opposite side (height of the building) is \(h\). So, \(\tan(57^{\circ})=\frac{h}{58}\).

Step2: Solve for \(h\)

We know that \(\tan(57^{\circ})\approx1.54\). Then \(h = 58\times\tan(57^{\circ})\). Substitute \(\tan(57^{\circ})\approx1.54\) into the equation: \(h=58\times1.54 = 89.32\)

Answer:

\(89.3\) ft