Question

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.
image of a right triangle with horizontal leg 88, vertical leg x (tree height), and angle of elevation 31° at the left vertex

Explanation:

Step1: Identify trigonometric ratio

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

Step2: Substitute values

$\tan(31^\circ) = \frac{x}{88}$

Step3: Solve for x

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

Step4: Calculate and round

$x \approx 88 \times 0.6009 \approx 53.0$

Answer:

53.0 feet