11. A vertical stick 10 cm long casts a shadow 8 cm long. At the same time, a tower casts a shadow 30 m long. Determine the height of the tower.
11. A vertical stick 10 cm long casts a shadow 8 cm long. At the same time, a tower casts a shadow 30 m long. Determine the height of the tower.

Solution:

Given:

Length of stick = 10cm

Length of the stick’s shadow = 8cm

Length of the tower’s shadow = 30m = 3000cm

To find:

The height of the tower = PQ.

In ΔABC ∼ ΔPQR

∠ABC = ∠PQR = 90o

∠ACB = ∠PRQ (Angular Elevation of Sun is same for a particular instant of time)

⇒ ΔABC ∼ ΔPQR    (By AA similarity)

AB/BC = PQ/QR (Corresponding sides are proportional)

10/8 = PQ/ 3000

PQ = (3000×10)/ 8

PQ = 30000/8

PQ = 3750/100

Therefore, PQ = 37.5 m