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 $30^o$. Find the height of the tower.
Given:
The angle of elevation of the top of tower, from the point on the ground and at a distance of 30 m from its foot, is $30^o$.
To find:
We have to find the height of tower.
Solution:
In the above image AB represents the tower, C is the point at a distance of $30\ m$ from foot of the tower and the angle of elevation of the top of tower from point C is $30^o$.
Let height of tower be $h$ metre
Now,
In $\triangle ABC$,
$tan\ 30^o\ =\ \frac{h}{30}$
$\Rightarrow \ \frac{1}{\sqrt{3}} \ =\ \frac{h}{30}$
$\Rightarrow \ h\ =\ \frac{30}{\sqrt{3} \ } \ =\ 10\sqrt{3}$
Therefore, the height of the tower is $10\sqrt{3}\ m$.
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