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

The tangent of an angle of elevation \(\theta\) in a right - triangle (where the height of the building is the opposite side \(y = 35\) ft and the horizontal distance is the adjacent side \(x=75\) ft) is given by \(\tan\theta=\frac{y}{x}\).
So, \(\tan\theta=\frac{35}{75}=\frac{7}{15}\approx0.4667\).

Step2: Find the angle using the inverse tangent function

We know that \(\theta=\tan^{- 1}(0.4667)\).
Using a calculator, \(\theta=\tan^{-1}(0.4667)\approx25.0^{\circ}\).

Answer:

\(25.0^{\circ}\)