# need a formula for triangle

• Dec 6th 2007, 07:00 AM
lostderiv
need a formula for triangle
hi i need to find the angle theta that maximizes the area of the isosceles triangle with legs length L. Once I can get a formula, I am fine to calculate the derivatives and determine the maximum, but my trig is a little rusty, especially with angles.
I need to know how to find the formula to express the area in terms of the angle, theta (theta is between the two identical sides of the isosceles).

thanks
• Dec 6th 2007, 07:23 AM
wingless
If length of two identical sides is L and the angle between them is θ, the area is $\displaystyle A = \frac {1}{2} L^2 sin(\theta)$
• Dec 6th 2007, 09:03 AM
lostderiv
alright, so next question
if i use the formula above to express area and take the derivative of said formula, will the derivative be cos(theta)? do I treat L as a constant?
• Dec 6th 2007, 10:13 AM
topsquark
Quote:

Originally Posted by lostderiv
if i use the formula above to express area and take the derivative of said formula, will the derivative be cos(theta)? do I treat L as a constant?

Quote:

Originally Posted by lostderiv
hi i need to find the angle theta that maximizes the area of the isosceles triangle with legs length L.

That seems to be the problem you posted, so I would say yes.

-Dan