Chapter 6.1, Problem 80PE

A woman participating in a triathlon can run $11\text{ ft/}\sec$ and swim $3\text{ ft/}\sec$ . She is at point $A$ , $900\text{ ft}$ from a straight shoreline and must swim to shore and run to point $B$ , $3000\text{ ft}$ down the beach.

a. Write an expression representing the total time t (in seconds) for her to get from point $A$ to point $B$ as a function of $\theta$ .

b. Use the TABLE function on a calculator to find the time $t$ for $\theta =0°,5°,10°,15°,20°,$ and $25°.$ Round to $1$ decimal place.

c. Which angle from part (b) gives the shortest total time?

d. Using calculus, we can show that the angle needed to minimize the total time is a solution to the equation $300\sec \theta \tan \theta -\frac{900}{11}{\sec }^2\theta =0$ . Solve the equation for $\theta$ , where $0°<\theta <90°$ Round to the nearest tenth of a degree.