Question

the angle of elevation to a nearby tree from a point on the ground is measured to be $31^{circ}$. how tall is the tree if the point on the ground is 88 feet from the bottom of the tree? round your answer to the nearest tenth of a foot if necessary.

Explanation:

Step1: Identify trigonometric relation

$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{x}{88}$

Step2: Substitute $\theta = 31^\circ$

$x = 88 \times \tan(31^\circ)$

Step3: Calculate the value

$x \approx 88 \times 0.6009 \approx 52.9$

Answer:

52.9 feet