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

Answer:

Height of building is 57.12 m.

Step-by-step 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:

$tan\theta =\dfrac{Perpendicular}{Base}$

$tanO =\dfrac{BT}{BO}\\\Rightarrow tan55^\circ = \dfrac{BT}{40}\\\Rightarrow BT = tan55^\circ \times 40\\\Rightarrow BT = 1.43\times 40\\\Rightarrow BT = 57.12 m$

So, height of building is 57.12 m.