Question

A $20m$ pole casts a $5m$ long shadow. If at the same time of the day, a building casts a shadow of $20m$, how high is the building?

• A. $400$ m
• B. $4$ m
• C. $80$ m
• D. $100$ m

Answer 1

The correct option is C $80$ m

Let the angle subtended between pole and shadow be $\theta$

$\Rightarrow$ $\tan \theta =\frac{20}{5}=4$

Similarly,

At same time of the day, angle subtended will remain same as position of sun is fixed.

Given that the shadow is $20m$ long.

Let height of the building be $x$

$\Rightarrow$ $\tan \theta =\frac{x}{20}=4$

$\Rightarrow x=80$ m