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.

Explanation:

Step1: Identify trigonometric ratio

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

Step2: Substitute values

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

Step3: Solve for x

$x=92\times\tan(22^\circ)$

Step4: Calculate value

$x\approx92\times0.4040=37.168$

Step5: Round to nearest hundredth

$x\approx37.17$

Answer:

37.17 feet