Question
From the top of a building, the angle of depression of
two cars on a straight road are 30° and 60° respectively. If the height of the building is 120 meters, find the distance between the two cars.Solution
Let the distance of the first car from the base of the building be x, and the distance of the second car be y. For the first car, using tan(30°) = height / distance: tan(30°) = 120 / x 1/√3 = 120 / x x = 120√3 meters. For the second car, using tan(60°) = height / distance: tan(60°) = 120 / y √3 = 120 / y y = 120 / √3 = 40√3 meters. The distance between the two cars is x - y: 120√3 - 40√3 = 80√3 meters. Correct answer: b
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