Angle that maximizes area of isosceles triangle with fixed leg length

[physstudent1]

Homework Statement

Find the angle theta that maximizes the area of an isosceles triangle whose legs have length l. The angle is the top angle if the left and right sides are l coming to a point with the bottom leg horizontal.

Homework Equations

The Attempt at a Solution

I broke the triangle up into two halves to use right angle trig and eventually got the area to equal A=l^2 * sin(theta/2)*cos(theta/2). When I took the derivative though I realized that I would have too many variables. I think there's a way to solve for l in terms of theta or theta in terms of l but I'm not sure how to do it can anyone point me in the right direction.

 

[Dick]

Why do you think you have to many variables? l is a constant. It's a constraint.

 

[physstudent1]

in that case I used 1/2*l^2*sin(theta) took the derivative got 1/2*l^2*cos(theta)=0 and got theta to be 90 degrees is this correct?

 

[Dick]

Yes, I think so.