Question

if a tree has a height of 31 feet, what would be the angle of elevation from level ground measured from 38 feet away? round your answer to the nearest tenth of a degree. answer submit answer

Explanation:

Step1: Set up the tangent ratio

In a right - triangle (where the height of the tree is the opposite side and the distance from the tree is the adjacent side), the tangent of the angle of elevation \(\theta\) is given by \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, the opposite side \(y = 31\) feet and the adjacent side \(x=38\) feet. So, \(\tan\theta=\frac{31}{38}\).

Step2: Solve for \(\theta\)

We know that \(\theta=\tan^{- 1}(\frac{31}{38})\). Using a calculator, \(\frac{31}{38}\approx0.8158\). Then \(\theta=\tan^{-1}(0.8158)\).
Calculating \(\tan^{-1}(0.8158)\) on a calculator (in degree mode), we get \(\theta\approx39.2^{\circ}\).

Answer:

\(39.2\)