2015 · Q43
An aeroplane flying at a height of 3000 m passes vertically above another aeroplane at an instant when the angles of elevation of the two planes from some point on the ground are 60° and 45° respectively. Then the vertical distance between the two planes is
Elementary MathematicsTrigonometry
- A1000({3} - 1) m
- B1000{3} m
- C1000(3 - {3}) m
- D3000{3} m
Explanation
With ground distance d: tan60 = 3000/d and tan45 = h/d, so h = 3000/sqrt(3) = 1000*sqrt(3) m; the gap is 3000 - 1000*sqrt(3) = 1000(3 - sqrt(3)) m. Hence option (c).