# Optimization problem..

• December 9th 2008, 10:05 PM
Manizzle
Optimization problem..
I just need help to set up this optimization problem..
There is an isosceles triangle inscribed in a circle that has a radius of 5, how can I express the area of the triangle ( $A = 1/2* bh$) in terms of the base of the triangle "b" or in terms of the height of the triangle "h"?
• December 10th 2008, 01:43 AM
tom@ballooncalculus
Use

$5 = \frac{b^2}{8h} + \frac{h}{2}$

(for which see Circle - Wikipedia, the free encyclopedia under "Sagitta properties")

and re-arrange to get either b or h in terms of the other.