Question

A vertical pole of $5.6m$ height casts a shadow $3.2m$ long. At the same time find
(i) find the length of the shadow cast by another pole $10.5m$ high
(ii) the height of a pole which can a shadow $5m$ long.

Answer 1

When the length of the pole is $5.6m,$ then the length of the shadow is $3.2m$

In triangle $DEC,$ we have

$\text{tan}C=\frac{DE}{EC}$

$\Rightarrow \text{tan}C=\frac{5.6}{3.2}$

$\Rightarrow \text{tan}C=1.75$

(i) Then if height $=10.5m$, then length of shadow is $BC.$

In triangle ABC, we have

$\text{tan}C=\frac{AB}{BC}$

$\Rightarrow 1.75=\frac{10.5}{BC}$

$\Rightarrow BC=\frac{10.5}{1.75}=6m$

(ii) If shadow length$=3.2$m, then height is given by

$\text{tan}C=\frac{\text{Height of pole}}{\text{Shadow length}}$

$\Rightarrow 1.75=\frac{\text{Height of pole}}{5}$

$\therefore \text{Height of pole}=1.75\times 5=8.75m$