A vertical stick 14 m long, casts a shadow 5 m long on the ground. At the same time, a tower casts a shadow of 44.5 m long on the ground. The height of the tower is _____.​

Correct option is A

Given:

Height of the stick = 14 m

Length of the shadow of the stick = 5 m

Length of the shadow of the tower = 44.5 m

Concept Used:

The problem involves similar triangles. The height of the stick and its shadow form one triangle, and the height of the tower and its shadow form another triangle.

The ratio of the height to the length of the shadow will be the same for both.

Formula Used:

Using the property of similar triangles:

​$$\frac{\text{Height of stick}}{\text{Length of shadow of stick}} = \frac{\text{Height of tower}}{\text{Length of shadow of tower}}$$​​

Solution:

Let the height of the tower be h.

​$$\frac{14}{5} = \frac{h}{44.5}$$​​

​$$h = \frac{44.5}{5} \times 14$$​​

​$$h = 8.9 \times 14 = 124.6$$​​

Thus, The height of the tower is 124.6 meters.