Question

question
if a tree has a height of 135 feet, what would be the angle of elevation from level ground
measured from 60 feet away? round your answer to the nearest tenth of a degree.
answer
attempt 2 out of 2
show examples

Explanation:

Step1: Identify the trigonometric ratio

We know that 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 ratio is given by $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, the height of the tree (opposite side) $y = 135$ feet and the adjacent side $x=60$ feet. So, $\tan\theta=\frac{135}{60}$.

Step2: Simplify the ratio

Simplify $\frac{135}{60}=\frac{9}{4}=2.25$.

Step3: Find the angle

We know that if $\tan\theta = 2.25$, then $\theta=\tan^{- 1}(2.25)$. Using a calculator, $\theta=\tan^{-1}(2.25)\approx66.0^{\circ}$ (rounded to the nearest tenth of a degree).

Answer:

$66.0^{\circ}$