Question

A pole of height $10m$ cast the shadow of length $12m$. Find the length of pole of it cast a shadow of length $15m$ at same time.

Answer 1

We have,

Pole of height $AB=10m$

Shadow of length $BC=12m$

Same time

Pole of height $AB=?$

Shadow of length $BC=15m$

In $\Delta ABC$

$\tan \theta =\frac{AB}{BC}=\frac{10}{12}$ …… (1)

$In\Delta ABC$

$\tan \theta =\frac{AB}{BC}=\frac{AB}{15}$ ……. (2)

Angle is equal in same time,

By equation (1) and (2) to, we get

$\frac{10}{12}=\frac{AB}{15}$

$AB=\frac{10\times 15}{12}$

$AB=\frac{10\times 5}{4}$

$AB=\frac{25}{2}=12.5m$

Hence, this is the answer.