If the angle of elevation of the top of a pillar from the ground level is raised from 30o to 60o, the length of the shadow of a pillar of height 50√3 will be decreased by

Given : CD is the pillar = $$50\sqrt{3}$$ m

To find : AB = $$x$$ = ?

Solution : In $$\triangle$$ BCD,

=> $$tan(60^\circ)=\frac{CD}{DB}$$

=> $$\sqrt{3}=\frac{50\sqrt{3}}{DB}$$

=> $$DB=\frac{50\sqrt{3}}{\sqrt{3}}$$

=> $$DB=50$$ -----------(i)

Again, in $$\triangle$$ ACD,

=> $$tan(30^\circ)=\frac{CD}{AD}$$

=> $$\frac{1}{\sqrt{3}}=\frac{50\sqrt{3}}{x+50}$$     [Using (i)]

=> $$x+50=50\sqrt{3} \times \sqrt{3}=150$$

=> $$x=150-50=100$$ m

=> Ans - (C)