Question

The angle of elevation of the top of a tower at any point on the ground is $\frac{\pi }{6}$ and after moving $20$ meters towards the tower it becomes $\pi 3$.The height of the tower is equal to :

• A. $10meters$
• B. $10\sqrt{3}meters$
• C. $\frac{10}{\sqrt{3}}meters$
• D. $5\sqrt{3}meters$

Answer 1

The correct option is B $10\sqrt{3}meters$

We can see from the diagram that $CD=20m$

Let $BC=xAB=h$

Now, in $△ABC$

$\tan {60}^O=\frac{h}{x}\Rightarrow x\sqrt{3}=h........................\left(1\right)\tan {30}^o=\frac{h}{x+20}\Rightarrow x+20=\sqrt{3}h\Rightarrow x+20=\sqrt{3}\ast x\sqrt{3}\Rightarrow x+20=3x\Rightarrow x=10$

from (1)

$h=x\sqrt{3}\Rightarrow h=10\sqrt{3}$