A balloon hovers directly above a point O on a straight level road. Two cars stand on the road on opposite sides of O, and from the balloon their angles of depression are 30° and 60°. If the cars are 100 m apart, the height of the balloon above the road is:

If the balloon is h m up, the cars are h·cot30° = h√3 and h·cot60° = h/√3 from O. Because they are on opposite sides these distances add: h√3 + h/√3 = 4h/√3 = 100, so h = 25√3 ≈ 43.3 m. The cars are then 75 m and 25 m from O, which do total 100 m. Placing both cars on the same side subtracts the distances and gives 50√3 ≈ 86.6 m, while 25 m and 75 m are the ground distances, not the height.