Question

The shadow of a tower is $15$ m when the Sun's altitude is ${30}^{\circ }$. What is the length of the shadow when the Sun's altitude is ${60}^{\circ }$?

• A. $3$ m
• B. $4$ m
• C. $5$ m
• D. $6$ m

Answer 1

The correct option is C $5$ m

Given, $OM=15$ m
Let $h$ be the height of the tower.
Therefore, $\frac{h}{15}=\tan {30}^{\circ }$
$\Rightarrow \frac{h}{ON}=\tan {60}^{\circ }$
$\Rightarrow \frac{\tan {30}^{\circ }}{\tan {60}^{\circ }}=\frac{h}{15}\times \frac{ON}{h}$
$\Rightarrow \frac{1}{\sqrt{3}}\cdot \frac{1}{\sqrt{3}}=\frac{ON}{15}$

$\Rightarrow ON=15÷3=5$

Thus length of the shadow is $5$ m.