Question

question
the angle of elevation to a nearby tree from a point on the ground is measured to be 22°. how tall is the tree if the point on the ground is 92 feet from the bottom of the tree? round your answer to the nearest hundredth of a foot if necessary.
answer attempt 1 out of 2

Explanation:

Step1: Identify trigonometric ratio

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

Step2: Substitute values

$\tan(22^\circ)=\frac{\text{height}}{92}$

Step3: Solve for height

$\text{height}=92\times\tan(22^\circ)$

Step4: Calculate and round

$\tan(22^\circ)\approx0.4040$, so $\text{height}\approx92\times0.4040\approx37.17$

Answer:

37.17