Question

a building that is 90 feet tall casts a shadow 30 feet long. what is the angle of elevation of the sun?
the angle of elevation is (square) degrees (round to the nearest tenth as needed)

Explanation:

Step1: Set up the tangent ratio

Let \(\theta\) be the angle of elevation. In a right - triangle formed by the building (opposite side \(a = 90\) feet) and its shadow (adjacent side \(b=30\) feet), the tangent of the angle of elevation is given by \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). So, \(\tan\theta=\frac{90}{30}\).

Step2: Calculate \(\tan\theta\)

\(\tan\theta = 3\).

Step3: Find \(\theta\)

Since \(\theta=\tan^{- 1}(3)\), using a calculator, \(\theta\approx71.6^{\circ}\) (rounded to the nearest tenth).

Answer:

\(71.6\)