If the angle of elevation of the sun changes from 30° to 45°, the length of the shadow of a pillar decreases by 80 m. The height of the pillar is:

Correct option is A

Given:

The angle of elevation of the sun changes from 30° to 45°, and the length of the shadow decreases by 80 m. 

Solution: 

Let the height of the pillar be h and the length of the shadow when the angle is 45° be x.

Then, when the angle is 30°, the shadow length becomes (x + 80).

Using trigonometric relations:

tan(45°) =$$\frac{h }{ x}$$​=> h = x

tan(30°) = $$\frac{h }{ (x + 80)}$$​​

Substitute h = x into the second equation:

tan(30°) = $$\frac{x }{ (x + 80)}$$​​

Now calculate tan(30°) and solve:

tan(30°) = $$\frac{1}{√3}$$​​

So, $$\frac{1}{√3} = \frac{x }{ (x + 80)}$$​​

x + 80 = $$\sqrt{3}$$x

$$\sqrt{3}$$​x -x =  80

x( $$\sqrt{3}$$​-1)=  80 

$$x = \frac{80}{\sqrt3-1} \\\ \\x= \frac{80}{\sqrt3-1} \times \frac{\sqrt3+1}{\sqrt3+1} \\\ \\ x = \frac{80(\sqrt3+1)}{2} \\\ \\x = 40(\sqrt3+1)$$​​