Question

If the elevation of the sun is ${30}^0$, then the length of the shadow cast by a tower of $150$ ft height is :

• A. $75\sqrt{3}$ ft.
• B. $200\sqrt{3}$ ft.
• C. $150\sqrt{3}$ ft.
• D. none of these

Answer 1

The correct option is C $150\sqrt{3}$ ft.

Let the height of the tower $AE=h=150ft.$ and $EC=x$

We can see that, in $△AEC,$

$\tan {30}^o=\frac{AE}{EC}=\frac{h}{x}$ {$\tan {30}^o=\frac{1}{\sqrt{3}}$}

$\Rightarrow x=h\sqrt{3}=150\sqrt{3}ft.$