# Optimisation problem: isoscles triangle inscribed in semi-circle

• Jul 4th 2009, 07:13 AM
banana_banana
Optimisation problem: isoscles triangle inscribed in semi-circle
4. Find the area of the largest isosceles triangle inscribed in a semi-circle of radius 10 ft, the vertex of the triangle being at the center of the circle.
• Jul 4th 2009, 07:22 AM
Hello banana_banana
Quote:

Originally Posted by banana_banana
4. Find the area of the largest isosceles triangle inscribed in a semi-circle of radius 10 ft, the vertex of the triangle being at the center of the circle.

Let the angle between the radii forming the two equal sides of the triangle be $\displaystyle \theta$. Then the area of the triangle is given by

$\displaystyle A = \tfrac12.10^2\sin\theta = 50\sin\theta$

$\displaystyle \Rightarrow \frac{dA}{d\theta} = 50\cos\theta = 0$ when $\displaystyle \theta = \tfrac{\pi}{2}$

Can you finish it now?

• Jul 4th 2009, 10:10 PM
banana_banana
> Optimisation problem: isoscles triangle inscribed in semi-circle
Quote:

Hello banana_bananaLet the angle between the radii forming the two equal sides of the triangle be $\displaystyle \theta$. Then the area of the triangle is given by

$\displaystyle A = \tfrac12.10^2\sin\theta = 50\sin\theta$

$\displaystyle \Rightarrow \frac{dA}{d\theta} = 50\cos\theta = 0$ when $\displaystyle \theta = \tfrac{\pi}{2}$

Can you finish it now?