Question

a person is standing exactly 36 ft from a telephone pole. there is a 30° angle of elevation from the ground to the top of the pole. what is the height of the pole?
○ 12 ft
○ 12√3 ft
○ 18 ft
○ 18√2 ft

Explanation:

Step1: Identify trigonometric relation

We have a right triangle, where the adjacent side (distance from person to pole) is 36 ft, the angle of elevation is \(30^\circ\), and we need to find the opposite side (height of pole, \(h\)). Use \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\).
\(\tan(30^\circ)=\frac{h}{36}\)

Step2: Solve for \(h\)

We know \(\tan(30^\circ)=\frac{1}{\sqrt{3}}\), so:
\(h = 36\times\tan(30^\circ)=36\times\frac{1}{\sqrt{3}}\)
Rationalize the denominator: \(h = \frac{36}{\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}}=\frac{36\sqrt{3}}{3}=12\sqrt{3}\)

Answer:

\(12\sqrt{3}\) ft