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.

> Optimisation problem: isoscles triangle inscribed in semi-circle

Quote:

Originally Posted by

**Grandad** 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?

Grandad

How can i finish? I am quite confused about this ? Would you like to explain it better?