Chapter 5.3, Problem 66E

APPLICATIONS

Rain Gutter 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 $\theta .$ (See the figure on the next page.)

(a) Show that the cross-sectional area of the gutter is modeled by the function $A\left(\theta \right)=100\sin \theta +100\sin \theta \cos \theta$.

(b) Graph the function $A$ for $0\le \theta \le \pi /2.$

(c) For what angle $\theta$ is the largest cross-sectional area achieved?