Answer:
magnitude: 31.13 km (nearest hundredth)
direction: [S 1.75° W] (nearest hundredth)
Step-by-step explanation:
[S 30° E] means 30° East of South
[S 25° W] means 25° West of South
The angle between the two directions (shown in orange as y on the attached diagram) = 180 - 30 - 25 = 125°
Now we can use the cosine rule to determine the magnitude (shown in blue on the attached diagram):
c² = a² + b² - 2ab cos C
⇒ c² = 15² + 20² - 2(15)(20) cos 125°
⇒ c² = 969.1458618...
⇒ c = 31.13110762...
⇒ c = 31.13 km (nearest hundredth)
Use the sine rule to determine the angle labelled pink on the attached diagram, then subtract 30° from this to find the direction of [S (x-30)° W]
sin(x) / 20 = sin(125) / 31.13110762...
⇒ sin(x) = 20 sin(125) / 31.13110762...
⇒ sin(x) =0.5262594921...
⇒ x = 31.7530704...°
Therefore, the angle of direction west of south = x - 30°
= 31.7530704...° - 30°
= 1.75° (nearest hundredth)
⇒ direction = [S 1.75° W]
