Question:
Choose the correct answer of the following question:
In the given figure, a tower $A B$ is $20 \mathrm{~m}$ high and $B C$, its shadow on the ground is $20 \sqrt{3} \mathrm{~m}$ long. The sun's altitude is
(a) 30° (b) 45° (c) 60° (d) none of these
Solution:
Let the sun's altitude be
We have,
$\mathrm{AB}=20 \mathrm{~m}$ and $\mathrm{BC}=20 \sqrt{3} \mathrm{~m}$
In $\Delta \mathrm{ABC}$,
$\tan \theta=\frac{\mathrm{AB}}{\mathrm{BC}}$
$\Rightarrow \tan \theta=\frac{20}{20 \sqrt{3}}$
$\Rightarrow \tan \theta=\frac{1}{\sqrt{3}}$
$\Rightarrow \tan \theta=\tan 30^{\circ}$
$\therefore \theta=30^{\circ}$
Hence, the correct answer is option (a).