A metal channel is formed by turning up the sides of width x of a rectangular sheet of metal through an angle theta. If the sheet is 200mm wide, determine the values of x and theta for which the cross-section of the channel will be a maximum. The answer from the book give x = 200/3 and theta = pi/3 but I have no idea how to go about solving this, any help would be appreciated thanks.
To start, draw the cross-sectional view. The sheet is 200 units wide, so label the turned-up sides with "x", the base with "200 - 2x", and the corners with "theta". If you draw a line across the top, what expression would stand for the area within?