Question

A flag pole $4m$ tall casts a $6m$ shadow. At the same time, a nearby building casts a shadow of $24m$. How tall is the building?

• A. $12m$
• B. $14m$
• C. $16m$
• D. $17m$

Answer 1

The correct option is C $16m$

In the above diagram

$AB$ is the building of height $h$

$DE$ is a flag pole of height $4m$

In $△DEC,\tan \theta =\frac{4}{6}=\frac{2}{3}$

In $△ABC,\tan \theta =\frac{h}{24}$

$⟹\frac{h}{24}=\frac{2}{3}$

$⟹h=16m$

So the height of the pole is $16m$