GIVEN: Angle of depression from an airplane to a point on the ground is 30° After travelling for 300 km, angle of depression of same point = 60° CONCEPT: Height and distance FORMULA USED:Tan θ = Perpendicular / Base CALCULATION:
AB = 300 km Let DE = x ∠BAE = ∠AEC = 30° ∠PBE = ∠BED = 60° Let AC = BD = h Now, Tan 60° = BD / DE = h/x ⇒ √3 = h/x ⇒ h = x√3 ---- (1) Tan 30° = AC / CE = h/(300 + x) ⇒ 1 / √3 = h / (300 + x) ⇒ h = (300 + x)/√3 ---- (2) From (1) and (2): (300 + x)/√3 = x√3 ⇒ 300 + x = 3x ⇒ 2x = 300 ⇒ x = 150 ∴ Required distance travelled by airplane = x = 150 km