Question

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.

Answer 1

Given: 

Length of stick = 10 cm 

Length of the stick’s shadow = 8 cm 

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

Required to find: the height of the tower = PQ.

In ΔABC ∼ ΔPQR 

∠ABC = ∠PQR = 90° 

∠ACB = ∠PRQ [Angular Elevation of Sun is same for a particular instant of time] 

⇒ ΔABC ∼ ΔPQR   [By AA similarity] 

So, we have 

\(\frac{AB}{BC}\) = \(\frac{PQ}{QR}\) [Corresponding sides are proportional] 

\(\frac{10}{8}\) = \(\frac{PQ}{3000}\)

PQ = \(\frac{(3000 \times10)}{8}\) 

PQ = \(\frac{30000}{8}\) 

PQ = \(\frac{3750}{100}\)

Therefore, PQ = 37.5 m