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Thread: Optimization problem

  1. December 7th 2008, 05:33 PM #1
    HMV
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    Optimization problem

    A photographer is taking a picture of a four-foot painting hung on the art gallery. The camera lens is 1 foot below the lower edge of the painting. How far should the camera be from the painting to maximize the angle subtended by the camera lens?
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  2. December 7th 2008, 05:52 PM #2
    galactus
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    Let x be the distance the camera is from the painting.

    Then, we have two triangles.

    Angle {\theta} is the one we need.

    So, we have tan^{-1}(\frac{5}{x})-tan^{-1}(\frac{1}{x})

    Differentiate, set to 0 and solve for x.

    We could also use cot:

    cot^{-1}(\frac{x}{5})-cot^{-1}(x)
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