Question

The angle of elevation of the top of a building from a point 50 m away from its foot is 60°. Find the height of the building.

Answer 1

Given: Angle of elevation = 60°, horizontal distance from foot = 50 m.

Step-wise calculation:

1. Let h be the height of the building.

In the right triangle formed.

`tan 60^circ = "Opposite"/"Adjacent"` 

= `h/50`

2. `tan 60^circ = sqrt(3)`. 

So, `sqrt(3) = h/50`.

3. `h = 50 xx sqrt(3)`.

Height = `50sqrt(3)` m ≈ 86.60 m to two decimal places.