Chapter 4.8, Problem 36E

(a)

To determine

To find: how far north and how far west is Reno relative to Miami.

Answer to Problem 36E

The Reno is 2434.44 west of Miami

Explanation of Solution

Given information:

A jet Reno, Nevada and heads toward Miami, Florida at a bearing of $100°$ . The distance between the two cities is approximately 2472 miles.

Calculation:

Consider a jet leaving Reno, Nevada and heading toward Miami, Florida at a bearing of $100°$

  

In air navigation, bearings are measured in degrees clockwise from north

Therefore, the bearing is $100°-90°=10°$

Therefore, in the north, the Reno is at the following distance from Miami

  $\begin{array}{c}2472\sin \left(10°\right)=240\times 0.1736\\ =429.26\end{array}$

Thus, the Reno is 429.26 mi north of Miami

Also, in the west, the Reno is at the following distance from Miami

  $\begin{array}{c}2472\cos \left(10°\right)=240\times 0.9848\\ =2434.44\end{array}$

Thus, the Reno is 2434.44 west of Miami.

(b)

To determine

To find: the bearing should it travel.

Answer to Problem 36E

The bearing is $280°$ .

Explanation of Solution

Given information:

Calculation:

If the jet is to travel directly from Miami to Reno, then the bearing is $270°+10°=280°$