The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. Find the height of the tower.
In right ABC, AB = height of the tower and point C is 30m away from the foot of the tower,
$\therefore \quad \mathrm{AC}=30 \mathrm{~m}$
$\operatorname{Now} \frac{\mathbf{A B}}{\mathbf{A C}}=\tan 30^{\circ}$
$\Rightarrow \frac{\mathbf{h}}{\mathbf{3 0}}=\frac{1}{\sqrt{\mathbf{3}}}$
$\left[\because \tan 30^{\circ}=\frac{\mathbf{1}}{\sqrt{\mathbf{3}}}\right]$
$\Rightarrow \mathrm{h}=\frac{\mathbf{3 0}}{\sqrt{3}}=\frac{\mathbf{3 0}}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}=10 \sqrt{3}$
Thus, the required height of the tower is $10 \sqrt{3} \mathrm{~m}$
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