The angle of elevation of the top of a tree from a point on the ground which is 300 m away from the tree is $30^\circ$. When the tree grew up, its angle of elevation of the top of it became $60^\circ$ from the same point. How much did the tree grow? (nearest to an integer)

346 m

⇒ In triangle ABC

⇒ tan\({30}^\circ\) = \(\frac{BC}{300}\)

⇒ \(\frac{1}{√3}\) = \(\frac{BC}{300}\)

⇒ BC = \(\frac{300}{√3}\) = 100\(\sqrt { 3}\)m

⇒ In triangle ABD

⇒ tan\({60}^\circ\) = \(\frac{BD}{300}\)

⇒ \(\sqrt { 3}\) = \(\frac{BD}{300}\)

⇒ BD = 300\(\sqrt { 3}\)m 

⇒ BD = BC + CD

⇒ 300\(\sqrt { 3}\) = 100\(\sqrt { 3}\) + CD

⇒ CD = 200\(\sqrt { 3}\) = 346m

Therefore, the tree grew near to 346m.