A balloon moving in a straight line passes vertically above two points A and B on a horizontal plane 10 f t apart. When above A the balloon has an angle of elevation of 60 o as seen from B . When above B it has an angle of elevation of 45 o as seen from A . The distance of B from the point C where it will touch the plane is

Step-by-step solution

In ∆ A B E , tan ⁡ 45 o = h 10 ⇒ h = 10 f t … … … . . i And in ∆ A B D , tan ⁡ 60 o = H 10 ⇒ H = 10 3 f t … … i i Also, H 10 + x = h B C (Similar triangle property) Using equation i and i i , we get, 10 3 10 + x = 10 x ⇒ 3 x = 10 + x ⇒ x = 10 3 - 1 = 5 3 + 1   f t