Question

From a balloon vertically above a straight road the angle of depression of two cars at an instance are 45 degree and 60 degree if the cards are hundred m apart find the height of the balloon

Answer 1

Let the two cars be at points C and D. That is distance between the cars, CD = 100 m Let BD = d Hence BC = (100 – x) m Let the height of the balloon be AB = ‘h’ m In right ΔABD, θ = 45°  In right ΔABC, θ = 60°  ⇒ 100√3 – √3h = h ⇒ 100√3 = √3h + h = h(√3 + 1)  ∴ h = 50√3(√3 + 1) m