The length of the shadow of a building is 100 meters, as shown below: the shadow of a building is 100 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 45 degrees. What is the height of the building?

Solution:

The diagram below is a schematic representation of the problem given. 

The length of the shadow is given by the side BC and its length is 100m. 

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

The angle which the tip of the building makes with the shadow is 45 degrees with the endpoint of the shadow. The angle ∠ACB is 45°.

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

  Tan θ = Perpendicular/Base 

Since  θ is 45°;  Perpendicular = AB = height of the building = h and BC = length of shadow = 100m  

We have,

Tan 45° = AB/BC

= h/100      

Since Tan 45° = 1

1 = h/100

h = 100 × 1 = 100 meters

The height of the building is h = 100 m

The length of the shadow of a building is 100 meters, as shown below: the shadow of a building is 100 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 45 degrees. What is the height of the building?

Summary:

If the building makes a shadow 100 meters long and the tip of the building makes an angle of 45 the height of the building is 100 meters.