Question

The angle of elevation and the angle of depression are ${30}^o$ and ${30}^o$ respectively when seen from the top of the first building to the top and base of the second building. If the distance between the bases of two building is 12 m, then find the height of big building.

• A. $16\sqrt{3}m$
• B. $12\sqrt{3}m$
• C. $14\sqrt{3}m$
• D. $20\sqrt{3}m$

Answer 1

The correct option is A $16\sqrt{3}m$

Given that the angle of elevation is ${30}^0$ and the angle of depression is ${30}^0$ when seen from the top of first building to the top and base of second building.

Let the height of first building be $x$ and the height of second building be $y$

From angle of depression ,we have $tan\left({30}^0\right)=\frac{12}{x}$

$\Rightarrow x=12cot\left({30}^0\right)=12\sqrt{3}$

From angle of elevation , we have $tan\left({30}^0\right)=\frac{y-x}{12}$

$\Rightarrow y-x=12tan\left({30}^0\right)=4\sqrt{3}$

$\Rightarrow y=x+4\sqrt{3}=16\sqrt{3}$