Answer: Ground Speed = 91 km/hr, Bearing = 189°
<u>Step-by-step explanation:</u>
Step 1: Draw a picture (see attached) to determine the angle between the given vectors. Notice that I moved the wind vector 180° <em>so the head of the wind vector would line up with the tail of the plane vector. </em>This created an angle of 34° between the plane and wind vectors. <em>Why?</em>
- the dashed line is 45°
- 79° (plane) - 45° (wind) = 34°
Step 2: Solve for the length of the resultant vector using Law of Cosines
<em>c² = a² + b² - ab cos C</em>
c² = (111)² + (25)² - (111)(25) cos 34°
c² = 12,946 - 4601
c² = 8345
c = 91
Ground speed is 91 km/hr
Step 3: Solve for the bearing of the resultant vector using Law of Sines
A = 9°
<em>Reminder that we moved the wind vector 180° to create the resultant vector so we need to add 180° to our answer.</em>
Bearing = A + 180°
= 9° + 180°
= 189°
