Question

By looking at the height of the chimney it is found that on walking towards it 50m in the horizontal line through its base, the angle of elevational of its top changes from ${30}^o$ to ${60}^o$. The height of the chimney is:

• A. $25m$
• B. $25\sqrt{2}$
• C. $25\sqrt{3}$
• D. None of these

Answer 1

Answer: (C)

$25\sqrt{3}$

Let feet of the chimney be point $D$

So by using trigonometry,

$\tan {60}^{\circ }=\frac{h}{BD}⟹BD=\frac{h}{\tan {60}^{\circ }}$

Also,

$\tan {30}^{\circ }=\frac{h}{AD}⟹AD=\frac{h}{\tan {30}^{\circ }}$

Now, $(AD-BD)=50=\frac{h}{\tan {30}^{\circ }}-\frac{h}{\tan {60}^{\circ }}$

$50=\sqrt{3}h-\frac{h}{\sqrt{3}}=\frac{2h}{\sqrt{3}}$

$h=25\sqrt{3}m$