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.