Hey there Purplemath! I need some help setting up the problem:
A rain gutter is to be constructed from a long 30 cm wide sheet of metal by bending two sides upwards at and angle of theta so that each of the sides and bottom is 10 cm wide. Determine the angle theta so that the cross-sectional area of the channel is maximum.
I drew a trapezoid with the long side (l1) at the top and the outside angle formed by the bottom of the trapezoid as theta. I have also labeled the bottom of the trapezoid as l2 and the height as h. I need help setting an equation to relate the area of the gutter with the angle theta. Not quire sure how to proceed. Thanks in advance!