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Trigonometry and Derivatives : Minimizing Distance

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A man is on an Island, 4 km from the nearest point P, on a straight shore. He wants to connect a cable from his present position to a point B , on the shore that is 9000 meters from P. The cable costs $5 per meter in the water and costs $3 per meter on shore. Where on the shore should the cable exit the water, so that the cable costs the least amount of money?

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Trigonometry and derivatives are used to minimize distance. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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