Question

A surveyor is 40m from the edge of a building. The angle of elevation from the surveyor to the top of the building is 55° . What is the height of the building?

Answer 1

Height of building is 57.12 m.

Explanation:

Let us try to understand the given dimensions as per the attached diagram.

Please refer to attached image (Right angled
`\triangle OBT`)

with
`\angle B =90^\circ`

Let O be the point where the Surveyor is standing.

B be the point of the base of building.

T be the point of top of building.

As per question statement,

`\angle O = 55^\circ`

Side OB = 40 m

To find: Side BT = ?

Using tangent trigonometric identity:

`tan\theta =(Perpendicular)/(Base)`

`tanO =(BT)/(BO)\\\Rightarrow tan55^\circ = (BT)/(40)\\\Rightarrow BT = tan55^\circ * 40\\\Rightarrow BT = 1.43* 40\\\Rightarrow BT = 57.12 m`

So, height of building is 57.12 m.