Example 2 :

Example 2: A plane flies at 300 miles per hour. There is a wind blowing out of the southeast at 86 miles per hour with a bearing of 320°. At what bearing must the plane head in order to have a true bearing (relative to the ground) of 14°? What will be the plane’s groundspeed (Figure  5)?

Figure 5
              Drawing for Example 2.

Use the law of sines to calculate the bearing and the groundspeed. Because these alternate interior angles are congruent, the 54° angle is the sum of the 14° angle and the 40° angle.

Therefore, the bearing of the plane should be 14° + 13.4° = 27.4°. The groundspeed of the plane is 342.3 miles per hour.

Any vector can be broken down into two component vectors, a horizontal component and a vertical component. These component vectors are called projections (Figure  6).

Figure 6
               Example of projections.