Calculus

The sun is setting at the rate of 1/4 deg/min, and appears to be dropping perpendicular to the horizon, as depicted in figure 6.2.5. How fast is the shadow of a 25 meter wall lengthening at the moment when the shadow is 50 meters long?

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  1. angle a = tan^-1 (.5)
    da/dt = -.25 deg/min = -.009436 radians/min

    x = 25 = y tan a
    y = 25/tan a
    dy/dt = -25 sec^2 a da/dt /tan^2 a

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  2. I can't see the diagram, but it appears that if the shadow is x, then

    25/x = tanθ

    so,

    -25/x^2 dx/dt = sec^2θ dθ/dt

    -25/2500 dx/dt = (1+1/4)(-1/4 * π/180)

    Now just solve for dx/dt

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