Question

The shadow of a tower is 30 meters when the sun's altitude is ${30}^{\circ }$. When the sun's altitude is ${60}^{\circ }$ then the length of shadow will be

• A. $60m$
• B. $15m$
• C. $10m$
• D. $5m$

Answer 1

The correct option is C $10m$

In fig. AB is the tower , BC is the length of the shadow of tower when altitude is ${30}^{\circ }$ i.e the angle of elevation of the top of the tower from the tip of the shadow is ${30}^{\circ }$ and DB is the length of the shadow, when the angle of elevation is ${60}^{\circ }$
Given, BC = 30 m
In $△ABC$
$\tan {30}^{\circ }=\frac{AB}{BC}$
$\Rightarrow \frac{1}{\sqrt{3}}=\frac{AB}{30}$
$\Rightarrow AB=\frac{30}{\sqrt{3}}=10\sqrt{3}m$
Now,
In $△ABD$
$\tan {60}^{\circ }=\frac{AB}{BD}$
$\Rightarrow \sqrt{3}=\frac{10\sqrt{3}}{BD}$
$\Rightarrow BD=10m$
Option C is correct.