Question:
If the altitude of the sum is at 60°, then the height of the vertical tower that will cast a shadow of length 30 m is
(a) $10 \sqrt{3} \mathrm{~m}$
(b) $15 \mathrm{~m}$
(c) $\frac{30}{\sqrt{3}} m$
(d) $15 \sqrt{2} \mathrm{~m}$
Solution:
Let 
be the height of vertical tower
Given that: altitude of sun is 
and shadow of length 
meters.
Here, we have to find the height of tower.
So we use trigonometric ratios.
In a triangle
,
$\Rightarrow \tan C=\frac{A B}{B C}$
$\Rightarrow \tan 60^{\circ}=\frac{A B}{B C}$
$\Rightarrow \sqrt{3}=\frac{h}{30}$
$\Rightarrow h=30 \sqrt{3}$
Hence the correct option is $a$.
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