The angle of elevation of a lamp post changes from 30° to 60° when a person walks 30 m towards it. Find the height of the lamp post.

Correct option is C

​Given:

Angle changes from 30^∘ to 60^∘

Distance walked = 30 m.

Formula Used: 

$$\tan \theta = \frac{Perpendicular}{base}$$ 

$$\tan 60\degree = \sqrt3 \\ \ \\ \tan 30\degree = \frac{1}{\sqrt 3}$$​​​

Solution: 

Let height = h:

​$$\tan(60^\circ) = \frac{h}{x}$$ = $$\sqrt{3}$$​

​$$\tan(30^\circ) = \frac{h}{x + 30}$$ = $$\frac{1}{\sqrt3}$$​​

So, 

$$h = \sqrt{3}x$$​:

Putting this in the $$\tan 30\degree$$​​

​$$\frac{\sqrt{3}x}{x + 30} = \frac{1}{\sqrt{3}}$$​​

​$$3x = x + 30 \\ x=15,$$​​

​$$h = 15\sqrt{3}$$​ m