Question

The height of the building is 100$\sqrt{3}$ft, What is the angle of elevation from a point on the level ground 100ft away from the base of the building?

• A. ${60}^{\circ }$
• B. ${30}^{\circ }$
• C. ${50}^{\circ }$
• D. ${70}^{\circ }$

Answer 1

The correct option is A

${60}^{\circ }$

Given the height of the building is 100$\sqrt{3}$ft. The point on the ground is 100ft away from the base of the building. This forms a standard trainslgular image.

The tan of the angle of elevation would be the ratio of the height of the building to the distance of the point from the base of the building.

Let the angle of elevation be x degrees.

Tanx = $\frac{100\sqrt{3}}{100}$

Tanx = $\sqrt{3}$

$ta{n}^{-1}$$\sqrt{3}$ = 60

Hence the angle of elevation is 60.