Question
A man observes the top of a tower at an angle of
elevation of 45°. He walks 50 meters towards the tower, and the angle of elevation becomes 60°. What is the height of the tower?Solution
Let the height of the tower be h, and the initial distance from the man to the tower be d. From the first observation: tan(45°) = h/d, so h = d. From the second observation: tan(60°) = h/(d - 50), so h/(d - 50) = √3. Substitute h = d into the second equation and solve to get h = 25(√3+3) meters. Correct option: a) 25(√3+3) meters
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