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 ft 18 ft ft

Answer 1

I believe option B ... 12 (square root of) 3 ft

Answer 2

Answer:

As per the statement:

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.

⇒Distance of a person from the telephone pole = 36 ft.

and angle of elevation ( $\theta$) = 30 degree.

We have to find the height of the pole.

Let h be the height of the pole.

Using tangent ratio:

$\tan \theta = \frac{\text{opposite side}}{\text{adjacent side}}$

Here,

Opposite side = h foot

Adjacent side = 36 ft

Angle of elevation: $\theta = 30^{\circ}$

Substitute these to solve for AB:

$\tan 30^{\circ} = \frac{h}{36}$

or

$h = 36\cdot \tan 30^{\circ}$

or

$h = 36\cdot \frac{1}{\sqrt{3}}$

Simplify:

$h = 12\sqrt{3}$ ft

Therefore, the height of the pole is $12\sqrt{3}$ ft