Question
There is a fire in the building. A man on the top of the
building see a Fire brigade van coming towards it. If it takes 8 minutes for the angle of depression to change from 30⁰ to 60⁰, how soon will the van reach the building?Solution
Let the height of the building be h. D the man standing on the top of the building. Now, from figure, AB = x and BC = y tan 60⁰ = h/y h = y√3 And tan 30⁰ = h/(x+y) 1/√3 = (y√3)/(x+y) 3y = x+y 2y = x y = x/2 Since, Time taken to cover a distance from A to B = 8 minutes ∴ Time taken to cover a unit distance = 8/x minutes For distance ‘y’ time taken = 8/x × y = 8/x × x/2 = 4 minutes.
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