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A simple question

dttom
in Mathematics

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The problem is not clear to me. Which parameter is varied, what is kept constant?

  • Author

e,a, and b is variables;

a+b=45 degree

0<=(a)<=45

e' date='a, and b is variables;

a+b=45 degree

0<=(a)<=45[/quote']

 

Where is e?

  • Author
Where is e?
Addition: AD=e

 

AD=e

You want the greatest possible value of AB*AC for this, because Area = AB*AC * sin(A)/2

AB = e cos(a)

AC = e cos(45-a)

AB*AC = e^2*cos(a)cos(45-a)

AB*AC*sin(A)/2 = e^2*cos(a)cos(45-a)sqrt(2)/4

The maximum is when a = 45 - a, or a = 22.5.

e^2*cos(22.5)^2*sqrt(2)/4 = e^2*(cos(45)+1)*sqrt(2)/8

= e^2*(1 + sqrt(2))/8

=Uncool=

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