Question

If the shadow of a building is 27 m when the Sun’s altitude is 30º, then the length of the shadow when the Sun’s altitude is 60º, is

• A. 6 m
• B. 9 m
• C. 15 m
• D. 27 m

Answer 1

The correct option is B 9 m

Let the building be AB.
Given that AB makes the shadow say, CB of length 27 m when the Sun’s altitude is 30° and it makes the shadow say, DB when the Sun’s altitude is 60º.
∴ CB = 27 m
$In\Delta ABC,$
$\tan {30}^{\circ }=\frac{AB}{CB}$
$\Rightarrow \frac{1}{\sqrt{3}}=\frac{AB}{27}$
$\Rightarrow AB=\frac{27}{\sqrt{3}}=9\sqrt{3}m$ ...(i)
Now, $in\Delta ABD,$
$\tan {60}^{\circ }=\frac{AB}{DB}$
$\Rightarrow \sqrt{3}=\frac{9\sqrt{3}}{DB}$ [From (i)]
$\Rightarrow DB=\frac{9\sqrt{3}}{\sqrt{3}}=9m$
Therefore, the length of the shadow is 9 m when the Sun’s altitude is 60°.
Hence, the correct answer is option (b).