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From problem set 4 unit 2C problem 10 I have some problems understanding the solution. The goal is to find the route that requires the minimum time to travel between to points. The equation to optimize is T=[(x^2+100^2)^1/2]/5+[((a-x)^2+100^2)^1/2]/2 .I differentiate obtaining the same result as the solution which is t prime equals to: [x/5(100^2+x^2)^1/2]+[a-x/2((a-x)^2+100^2)^1/2]. At this point the solution substitutes both terms with sin, but both numerators are adjacent side to the angles not opposite.. Could someone please help me understand better this problem? Thank you in advance

OCW Scholar - Single Variable Calculus
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We get this question here about once a week, because the problem and solution given in the materials are erroneous. The most important errors in the problem was labeling the wrong angles alpha and beta, which should instead be angles made with a line perpendicular to the shore rather than angles made with the shore. The error switches the result to cosine because the sine of an angle equals the cosine of its complement. Here's a corrected version of the problem and solution: http://assets.openstudy.com/updates/attachments/522ad142e4b0a8663d5580c8-creeksider-1378561866464-2c10corrected.pdf
thank you

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