Question

the angle of elevation to a nearby tree from a point on the ground is measured to be 26°. how tall is the tree if the point on the ground is 91 feet from the bottom of the tree? round your answer to the nearest tenth of a foot if necessary.

Explanation:

Step1: Identify trigonometric relationship

The tree height is opposite side, distance is adjacent side to angle \(x = 26^\circ\). Use tangent: \(\tan(x) = \frac{\text{opposite}}{\text{adjacent}}\)

Step2: Rearrange to find height

Let height = \(h\), adjacent = 91 ft. So \(h = 91 \times \tan(26^\circ)\)

Step3: Calculate the value

\(\tan(26^\circ) \approx 0.4877\), so \(h \approx 91 \times 0.4877 \approx 44.38\)

Answer:

44.4