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Math Help - Where should the point P be chosenon the line AB so as to maximize the angle theta

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    Red face Where should the point P be chosenon the line AB so as to maximize the angle theta

    http://i1183.photobucket.com/albums/...rea/4-7-69.gif

    "Where should the point P be chosenon the line AB so as to maximize the angle theta"
    how would i do this question?

    will this work?: t = t1 + t2
    tan t1=BP/BC (where C= the angle between B and P)
    t1=arctan(BP/BC)
    tan t2=AP/AD (where D= the angle between A and P)
    t2=arctan(AP/AD)

    sum= t1 + t2 --> arctan(BP/BC)+arctan(AP/AD)

    then add in the known values:

    t1 + t2= arctan(BP/2)+arctan(AP/5)

    t= arctan((1/2)BP)+arctan((1/5)AP)

    since we know AP+BP=3....solve for BP.
    BP=-AP+3 and then substitute into the equation above:

    t= arctan((1/2)(-AP+3))+arctan((1/5)AP)
    t= -arctan((1/2AP-3/2))+arctan((1/5)AP)...then found the derivative

    y= -1/(2(1+(1/2)AP-(3/2))^2) + 1/(5(1+(1/25)AP)^2)

    i then solved for AP

    and got 5+2sqrt(5)=9.472
    and 5-2sqrt(5)=.5279
    and my answer was .5279

    is that correct?

    *btw, AP+BP=3....because in the image it just shows the AP=3, when it should be that whole side=3.
    Last edited by mr fantastic; April 19th 2011 at 05:40 AM. Reason: Re-titled.
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