Two men standing on same side of a pillar 75 metre high, observe the angles of elevation of the top of the pillar to be 30° and 60° respectively the distance between two men is

Given : CD is the pillar = 75 m

To find : AB = $$x$$ = ?

Solution : In $$\triangle$$ BCD,

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

=> $$\sqrt{3}=\frac{75}{DB}$$

=> $$DB=\frac{75}{\sqrt{3}}$$

=> $$DB=25\sqrt{3}$$ -----------(i)

Again, in $$\triangle$$ ACD,

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

=> $$\frac{1}{\sqrt{3}}=\frac{75}{x+25\sqrt{3}}$$     [Using (i)]

=> $$x+25\sqrt{3}=75\sqrt{3}$$

=> $$x=75\sqrt{3}-25\sqrt{3}=50\sqrt{3}$$ m

=> Ans - (A)