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.

AcademicMathematicsNCERTClass 10

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 $10\sqrt{3}\ m$.

raja
Updated on 10-Oct-2022 13:23:30

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