1. ## Optimization with trigs.

A rain gutter is to be constructed from a metal sheet of width 30 cm by bending up one-third of the sheet on each side through an angle of theta. How should theta be chosen so that the gutter will carry the maximum amount of water?

2. Originally Posted by a.a
A rain gutter is to be constructed from a metal sheet of width 30 cm by bending up one-third of the sheet on each side through an angle of theta. How should theta be chosen so that the gutter will carry the maximum amount of water?
You want max area of the triangle formed by the fold...does that help?

3. this is all i could come up with so far but mu solutions dont make sence because they dont fall into the possible domain of theta greater than or equal to 0 and less than or equal to 90.

A(theta) = 100 sin theta + 100 cos theta sin theta

i found and simplified for A' and got
A'= cos 2theta + cos theta

4. so instead of finding A of the trapazoid solve max area of triangle?

5. Originally Posted by a.a
this is all i could come up with so far but mu solutions dont make sence because they dont fall into the possible domain of theta greater than or equal to 0 and less than or equal to 90.

A(theta) = 100 sin theta + 100 cos theta sin theta

i found and simplified for A' and got
A'= cos 2theta + cos theta
maybe this will be of some help...the max of $\displaystyle a\cdot{cos(x)}+b\cdot{sin(x)}$ is $\displaystyle \sqrt{a^2+b^2}$ so in this case it would be $\displaystyle 100\sqrt{2}$