The angle of elevation of the top of a small tree from a point on the ground 300m away from the foot of the tree was 30°. When the tree grew taller, its angle of elevation became 60° from the same point. By how much did the tree grow?

Correct option is B

​Given:

Distance from the tree = 300 m

Initial angle of elevation = 30^∘

Final angle of elevation = 60^∘

Formula Used:

​$$\tan 30\degree= \frac{1}{\sqrt3} , \ \ \ \ \tan 60\degree = \sqrt3$$​​

​$$\text{Height of tree} = \text{Distance from base} \times \tan(\text{angle of elevation}).$$​​

Solution: ​

Now, 

Height before growth:

$$h_1 = 300 \times \tan 30^\circ = \frac{300}{\sqrt{3}} \text{m}.$$​​

Height after growth:

$$h_2 = 300 \times \tan 60^\circ = 300 \sqrt{3}\ m$$​​

Tree growth:

$$\text{Growth} = h_2 - h_1 = 300 \sqrt{3} - \frac{300}{\sqrt{3}} = 200 \sqrt{3}$$​​