A person 6 feet tall walks at a rate of 150 feet per minute toward a light tower whose searchlight is located 40 feet above the ground. Find the rate that the length of the shadow is changing.

Answer 1

Draw a diagram. If the man is x feet from the tower, and his shadow is s ft long, then using similar triangles,

s/6 = (x+s)/40
s = 3/17 x

ds/dt = 3/17 dx/dt

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