Optimization isosceles triangle problem

  • #1
270
1

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 theres 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.
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,263
619
Why do you think you have to many variables? l is a constant. It's a constraint.
 
  • #3
270
1
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?
 
  • #4
Dick
Science Advisor
Homework Helper
26,263
619
Yes, I think so.
 

Related Threads on Optimization isosceles triangle problem

  • Last Post
Replies
2
Views
4K
Replies
5
Views
8K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
1
Views
2K
Replies
5
Views
8K
Replies
7
Views
4K
Replies
2
Views
11K
Replies
2
Views
5K
Replies
1
Views
5K
Top