Question

What is the height of the pole? 12 ft 12 StartRoot 3 EndRoot ft 18 ft 18 StartRoot 2 EndRoot ft.

Answer 1

You can use tangent trigonometric ratio since that deals with perpendicular and base and since the case is related physically to right triangle, thus it would be useful here.

The height of the considered pole is given by Option B:  $12\sqrt3$

Given that:

• The person is standing 36 feet away from base of a pole.
• The angle of elevation from base of person to top of pole is 30 degrees.

To find:

Height of pole.

Using tangent ratio to find height of pole:

Let the height of the pole be x.

In the given figure attached below, we can see that there is a right angled triangle ABC forming.

By using the tangent ratio from angle C, we have:

$\tan(30^\circ) = \dfrac{\text{AB}}{\text{BC}} = \dfrac{x}{36}\\\dfrac{1}{\sqrt{3}} = \dfrac{x}{36}\\\\x= \dfrac{36}{\sqrt3}\\x = \dfrac{ 12 \times \sqrt3 \times \sqrt 3}{\sqrt3} = 12\sqrt3$

Thus, the height of the considered pole is given by Option B:  $12\sqrt3$

Learn more about trigonometry and tangent ratio here:

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