Choose the correct answer of the following question:

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 θ">θ

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).

 

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