Question

question if a tree has a height of 125 feet, what would be the angle of elevation from level ground measured from 98 feet away? round your answer to the nearest tenth of a degree. answer attempt 1 out of 2

Explanation:

Step1: Recall the tangent - ratio formula

We know that in a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, the height of the tree is the opposite side ($a = 125$ feet) and the distance from the tree is the adjacent side ($b = 98$ feet). So, $\tan\theta=\frac{125}{98}$.

Step2: Calculate the angle

We need to find $\theta$. Using the inverse - tangent function, $\theta=\tan^{- 1}(\frac{125}{98})$.
$\theta=\tan^{-1}(1.27551)$.
Using a calculator, $\theta\approx52.0^{\circ}$.

Answer:

$52.0^{\circ}$