NTA Abhyas JEE Main2020MathematicsHeights and DistancesPractice
A balloon moving in a straight line passes vertically above two points A and B on a horizontal plane 300 ft apart. When above A it has an altitude of 45 o as seen from B . When above B it has an altitude of 30 o as seen from A . The distance of B from the point C where it will touch the plane is
Options
- A150 3 + 1 f t
- B150 f t
- C150 3 + 3 f t
- D300 3 + 1 f t
Correct answer
A. 150 3 + 1 f t
Step-by-step solution
In ∆ ABE , tan ⁡ 30 o = h 300 ⇒ h = 100 3 f t … 1 and in Δ A B D , tan ⁡ 45 o = H 300 ⇒ H = 300 f t … 2 Also, H A C = h B C (Similar triangles) ⇒ 300 300 + x = 100 3 x [using Eq. 1 and 2 ] ⇒ 3 x = 300 + x ⇒ x = 300 3 - 1 = 150 3 + 1   f t .