Question

At a point 400 feet from the base of a building, the angle of elevation to the top of the building is 60◦. Find the height of the building (leave your answer in radical form)

Answer 1

Answer:

The height of the building is 400√3

Step-by-step explanation:

Given:

Angle of elevation to the top of the building = 60°

Distance from the observer to the base of it = 400 ft

We have to find the height of the building.

Let the height of the building be "h" ft

Using trigonometric ratio:

⇒ $tan(\theta)=\frac{opposite}{adjacent}$

So,

Considering adjacent side as 400 ft.

⇒ $tan(\theta) =\frac{h}{400}$

⇒ $h=tan(\theta)\times 400$

⇒ $h=tan(60)\times 400$

⇒ $h=\sqrt{3} \times 400$                         ...tan(60) = √3

⇒ $h=400\sqrt{3}$ ft

The height of the building is 400 Sq-rt (3) ft in terms of radical form and in decimals it is 692.8 ft.