Question

The angle of elevation of the top of a tree from a point A on the ground is ${60}^{\circ }$ . On walking 20 m away from its base, to a point B, the angle of elevation changes to ${30}^{\circ }$. Find the height of the tree.

• A. $10\sqrt{3}$
• B. $20\sqrt{3}$
• C. $30\sqrt{3}$
• D. $40\sqrt{3}$

Answer 1

The correct option is A

$10\sqrt{3}$

In triangle ACD,

$\tan \theta =\frac{DC}{CA}=\frac{h}{x}$

$\Rightarrow \tan {60}^{\circ }=\sqrt{3}=\frac{h}{x}$ ..................... 1

In triangle CDB,

$\Rightarrow \tan {30}^{\circ }=\frac{CD}{CB}$

$\Rightarrow \frac{1}{\sqrt{3}}=\frac{h}{x+20}$.......................2

Solving 1 and 2, we get $h=10\sqrt{3}m$
Thus, the height of the tree is $10\sqrt{3}m$.