Question

A vertical stick $1m$ long casts a shadow $80cm$ long. At the same time, a tower casts a shadow $30m$ long. Determine the height of the tower.

Answer 1

Step 1:Analyse the given data

Length of stick $=1m=100cm$

Length of the shadow of the stick $=80cm$

The tower casts a shadow $30m=3000cm$

Length of the tower $=hcm$

Step 2: Use the AA similarity theorem to find the height of the tower:

Let, us consider the figure given below:

In $△ABC$ and $△PQR$

$\angle B=\angle Q={90}^{°}$

$\angle C=\angle R$ (angular elevation of the sun)

Thus, $△ABC~△PQR$ (By AA similarity)

$$\begin{gathered} \Rightarrow \frac{AB}{PQ}=\frac{BC}{QR} \\ \Rightarrow \frac{100}{h}=\frac{80}{3000} \\ \Rightarrow h=\frac{100}{80}\times 3000 \\ \Rightarrow h=\frac{10}{8}\times 3000 \\ \Rightarrow h=3750cm \\ \Rightarrow h=37.5m \end{gathered}$$

Hence, the height of the tower is.$37.5m$