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)
Answer & explanation
Correct answer: option 4
⇒ 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.