A 5 meter tall tree casts a shadow of 12 meter. At the same time, a nearby tower casts a shadow of 48 meter. Find the height of the tower.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 20 meter
At the same time the sun’s rays fall on both objects at the same angle, so each object, its shadow and the ray form similar right triangles. In similar triangles the ratio of height to shadow is the same.
Height to shadow is the same for both: \(\displaystyle\frac{h}{48}=\frac{5}{12}\)
Height of the tower: \(\displaystyle h=\frac{5\times48}{12}=20\) m