Question

3
note: figure not drawn to scale.
shana is creating an estimate for trimming the tree shown above, but needs to determine its height. at a distance of 30 ft from the base of the tree, she measures the angle of elevation to the top of the tree to be 63°.
what is the approximate height of the tree?
a. 15.29 ft
b. 13.62 ft
c. 26.73 ft
d. 58.88 ft

Explanation:

Step1: Identify the trigonometric relationship

We have a right triangle where the adjacent side to the angle of elevation ($63^\circ$) is 30 ft (distance from the base), and the opposite side is the height ($h$) of the tree. We use the tangent function, which is defined as $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$. So, $\tan(63^\circ)=\frac{h}{30}$.

Step2: Solve for the height

Rearrange the formula to solve for $h$: $h = 30\times\tan(63^\circ)$. Calculate $\tan(63^\circ)\approx1.9626$. Then, $h = 30\times1.9626 = 58.878\approx58.88$ ft. Wait, no, wait, that can't be right. Wait, maybe I made a mistake. Wait, no, let's check again. Wait, $\tan(63^\circ)$ is approximately 1.9626, so 301.9626 is about 58.88. But wait, the options have D as 58.88 ft. But wait, maybe I mixed up the angle? Wait, no, the angle of elevation is 63 degrees, adjacent is 30 ft. Wait, but let's check the options. Wait, maybe I miscalculated. Wait, no, $\tan(63^\circ)\approx1.9626$, so 301.9626 is 58.878, which is approximately 58.88 ft. So the answer should be D. Wait, but wait, maybe the angle is 36 degrees? No, the problem says 63 degrees. Wait, let's confirm the tangent of 63 degrees. Using a calculator, $\tan(63^\circ)\approx1.9626105055$. So 30*1.9626105055 = 58.878315165, which is approximately 58.88 ft. So the correct answer is D.

Answer:

D. 58.88 ft