Question
From a point on the ground, the angle of elevation of
the top of a building is 45°. After walking 10 meters towards the building, the angle of elevation increases to 60°. Find the height of the building.Solution
Let the height of the building be h meters. Let the initial distance from the building be x meters. From the first position: tan 45° = h/x, 1 = h/x, h = x. From the second position (after moving 10 meters closer): tan 60° = h/(x - 10), √3 = h/(x - 10). Now substitute h = x into the second equation: √3 = x/(x - 10). Solving this equation: x/√3 = x - 10 x(√3 - 1)/ √3 = 10 x = 10 (√3 - 1)/ √3 meters. So, the height of the building h = 10 (√3 - 1)/ √3 meters.
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