Question

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

• A. 100 cm
• B. 75 cm
• C. 65 cm
• D. 37.5 cm

Answer 1

The correct option is D

37.5 cm

The above figure represents vertical stick of 10 cm and shadow cast by it. So,
$\tan \theta =\frac{10}{8}=\frac{5}{4}$

The second figure represents a tower that casts a shodow of 30 cm long.
As both the shadows are formed at the same time, the sun rays forms the same angle in both the cases.
$\tan \theta =\frac{h}{30}$

$\frac{5}{4}=\frac{h}{30}$

h = 37.5 cm