Chapter 5.6, Problem 33E

(a)

To determine

To find: The distance of the flight.

Answer to Problem 33E

227.7 miles

Explanation of Solution

Given information: Air Travel: In order to avoid a storm, a pilot starts the flight ${13}^{\circ }$ off course. After flying 80 miles in this direction, the pilot turns the plane to head toward the destination. The angle formed by the course of the plane during the first part of the flight and the course during the second part of the flight is ${160}^{\circ }$ .

Calculation:

The triangle is drawn with the third angle figured out. We are looking for the actual flight length in part a and the direct flight length he could have taken if there were no storm in part b. but we will eventually need to know all leg’s lengths.

By law of sines,

  $\begin{array}{l}\frac{80}{\sin 7^{\circ }}=\frac{x}{\sin {13}^{\circ }}=\frac{d}{\sin {160}^{\circ }}\\ x=\frac{80\times \sin {13}^{\circ }}{\sin 7^{\circ }}=147.7\end{array}$

So the length of the trip was:

  $147.7+80=227.7\text{ miles}$

(b)

To determine

To find: The distance of a direct flight to the destination.

Answer to Problem 33E

224.5 miles

Explanation of Solution

Given information: Air Travel: In order to avoid a storm, a pilot starts the flight ${13}^{\circ }$ off course. After flying 80 miles in this direction, the pilot turns the plane to head toward the destination. The angle formed by the course of the plane during the first part of the flight and the course during the second part of the flight is ${160}^{\circ }$ .

Calculation:

The triangle is drawn with the third angle figured out. We are looking for the actual flight length in part a and the direct flight length he could have taken if there were no storm in part b. but we will eventually need to know all leg’s lengths.

By law of sines,

  $\begin{array}{l}\frac{80}{\sin 7^{\circ }}=\frac{x}{\sin {13}^{\circ }}=\frac{d}{\sin {160}^{\circ }}\\ d=\frac{80\times \sin {160}^{\circ }}{\sin 7^{\circ }}=224.5\end{array}$

So the total length of a direct trip would be 224.5 miles.