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? 18√2 ft 18 ft 12√3 ft 12 ft

Explanation:

Step1: Use tangent function

\(\tan\theta=\frac{opposite}{adjacent}\), where \(\theta = 30^{\circ}\) and adjacent = 36 ft.
\(\tan30^{\circ}=\frac{h}{36}\) (h is height of pole).

Step2: Solve for h

Since \(\tan30^{\circ}=\frac{\sqrt{3}}{3}\), then \(h = 36\times\tan30^{\circ}=36\times\frac{\sqrt{3}}{3}=12\sqrt{3}\) ft.

Answer:

\(12\sqrt{3}\text{ ft}\)