1. A rain gutter is to be constructed from a length of sheet metal that is 24cm wide. TO form the gutter the width is folded along its length in three equal sections, so that both ends form an angle theta with the middle section (horizontal). Find the angle that will maximize the capacity of the rain gutter.

I know that you must find the absolute maximum value of theta in the function which would just be taking the first derivative and letting theta = 0 or doesn't exist.

I used one of the triangle identities of 2^2= 3 + 1 to make it into:

8^2=(4sqrt3)^2 + 4^2

However the question does not provide the original function but rather I am supposed to construct in terms of theta. and I have no clue how to do this.

Any help would be greatly appreciated.