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.

• A. 35.4 cm
• B. 30 cm
• C. 37.5 cm
• D. 39.7 cm

Answer 1

The correct option is C 37.5 cm

In ΔABC and ΔPQR
∠ABC = ∠PQR $={90}^{\circ }$
∠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]

Now,
$\Rightarrow \frac{10}{8}=\frac{PQ}{3000}$
$\Rightarrow PQ=\frac{(3000\times 10)}{8}$
$\Rightarrow PQ=\frac{30000}{8}$
$\Rightarrow PQ=\frac{3750}{100}$

Therefore, PQ = 37.5 m