Question

Question 15
A vertical pole of a length 6 m casts a shadow 4m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.

Answer 1

Length of the vertical pole = 6m (Given)
Length of the shadow of the pole = 4 m (Given)
Let Height of tower = h m
Length of shadow of the tower = 28 m (Given)
In $\Delta ABCand\Delta DEF$,
$\angle C=\angle E\left(angularelevation\right)$
$\angle B=\angle F={90}^{\circ }$
$\therefore \Delta ABC\sim \Delta DFE$ (By AAA similarity criterion)
$\therefore \frac{AB}{DF}=\frac{BC}{EF}$ (If two triangles are similar then their corresponding sides are proportional.)
$\therefore \frac{6}{h}=\frac{4}{28}$
$\Rightarrow h=6\times \frac{28}{4}$
$\Rightarrow h=6\times 7$
$\Rightarrow h=42m$
Hence, the height of the tower is 42 m.