Question

A vertical pole of length 7.5cm casts a shadow 5m long on the ground and at the same time a tower casts a shadow 24m long. Find the height of the tower.

Answer 1

Let AB be the vertical stick and BC be its shadow. 

Given: 

AB = 7.5 m, BC = 5 m

Let PQ be the tower and QR be its shadow. 

Given: 

QR = 24 m 

Let the length of PQ be x m. 

In ∆ ABC and ∆ PQR, we have: 

∠ABC = ∠PQR = 90°

∠ACB = ∠PRQ (Angular elevation of the sun at the same time) 

Therefore, by AA similarity theorem , we get : 

∆ ABC ~ ∆ PQR 

⇒ AB/BC = PQ/QR 

⇒ 7.5/5 = x/24 

x = 7.5/5 x 36 cm

Therefore, PQ = 36 m 

Hence, the height of the tower is 36 m.