A man is flying in a hot-air balloon in a straight line at a constant rate of 4 feet per second, while keeping it at a constant altitude. As he approaches the parking lot of a market, he notices that the angle of depression from his balloon to a friend's car in the parking lot is 34 degrees. A minute and a half later, after flying directly over this friend's car, he looks back to see his friend getting into the car and observes the angle of depression to be 36 degrees . At that time, what is the distance between him and his friend? (Give your answer to the nearest foot.)
Answer 239.
Let x = horizontal distance from a point over the friend's car initially
=> x - 4 * (1.5*60) = horizontal distance from a point over the friend's car after 1.5 minutes
Let h = height directly over the friend's car of the altitude of flying
=> x/h = cot34° and (x - 360)/h = cot36°
=> [x - (x - 360)]/h = cot34° - cot36°
=> h = 360 * (cot34° - cot36°) = 38.22 ft.
=> distance of the balloon from the car at the end of 1.5 minutes
= hcosec36°
= 38.22cosec36°
= 65 ft.
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