Question

what is the angle of elevation to the nearest tenth of a degree to the top of a 35 - ft building from 75 ft away?
angle of elevation =

Explanation:

Step1: Recall the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, the height of the building (opposite side) \(h = 35\) ft and the horizontal distance (adjacent side) \(d=75\) ft. So, \(\tan\theta=\frac{35}{75}\).

Step2: Calculate the angle

\(\theta=\tan^{- 1}(\frac{35}{75})\). Using a calculator, \(\frac{35}{75}\approx0.4667\). Then \(\theta=\tan^{-1}(0.4667)\approx25.0^{\circ}\)

Answer:

\(25.0^{\circ}\)