The length of the shadow of a building is 120 meters, as shown below. The shadow of a building is 120 meters long. The acute angle that the shadow makes with the line joining the tip of the building to the end of the shadow measures 60 degrees. What is the height of the building?

Solution:

The length of the shadow is given by the side CB and its length is 120m. 

The height of the building is represented by AC and it is ‘ h ‘.

The angle which the tip of the building makes with the shadow is 60 degrees with the endpoint of the shadow. The angle ∠ABC is 60°.

To find the height of the building the tanθ trigonometric relationship is used :

  Tan θ = Perpendicular/Base 

Since  θ is 60°;  Perpendicular = AC = height of the building = h and CB = length of shadow = 120m  

We have,

Tan 60° = AC/CB

= h/120

Since Tan 60° = √3

√3  =  h/120

h = 120 × √3 = 120√3 metres

The height of the building is h = 120√3 m

The length of the shadow of a building is 120 meters, as shown below. The shadow of a building is 120 meters long. The acute angle that the shadow makes with the line joining the tip of the building to the end of the shadow measures 60 degrees. What is the height of the building?

Summary:

If the building makes a shadow 120 meters long and the tip of the building makes an angle of 60° the height of the building is 120√3 meters.