## anonymous 5 years ago The cross section of a trough is an inverted isosceles triangle. Prove that the trough has maximum capacity when the vertex angle is pi/2rad.

1. anonymous

Define the cross sectional area in terms of the vertex angle (assuming the sides are a constant length. Differentiate to find the stationary points and prove pi/2 is a max.

2. anonymous

Note that the area of a triangle with sides a,b,c, with the angle C between a and b has an area: $\text{Area} = \frac{1}{2}\cdot a\ \cdot b\ \cdot \sin C$

3. anonymous

so differentiate 1/2ab sinc? that become 1/2ab cosc??