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?

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- Apr 20th 2008, 06:35 PMa.aOptimization 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?

- Apr 20th 2008, 06:37 PMMathstud28
- Apr 20th 2008, 06:38 PMa.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 - Apr 20th 2008, 06:39 PMa.a
so instead of finding A of the trapazoid solve max area of triangle?

- Apr 20th 2008, 06:40 PMMathstud28