Problem $3$: $(25$ points$)$

A ditch with a rectangular cross$-$section of $30$ square feet and $200$ foot in length $(6,000f{t}^3$ bank$)$ is planned. The soil's angle of repose is $25$ degrees and the swell $\%$ is $20\%.$ Find the height and width of the spoil bank. Assume the pile is $100$ ft long.