An airplane flies 200 km due west from city A to City B and them 300 km in the direction of 30.0 degrees north of west from city B to city C. In straight-line distance, how far is city C from city A? Relative to city A, in what direction is city C?

Answer 1

Calculate the cumulative coordinates of B and C relative to A by resolving the distances into X(east) and Y(north) components.
From A to B, distance Db = 200 km,
direction = 180 degrees.
x=Db.cos(180)=-200
y=Db.sin(180)=0
Therefore the coordinates of B relative to A are (-200,0).

From B to C:
Distance Dc = 300 km
direction = 180-30=150 degrees.
x=300 cos(150)=-259.81 km
y=300 sin(150)=150 km
The coordinates of C relative to B are (-259.81, 150).

The cumulative coordinate relative to A are
(-200+(-259.81), 0+150)
=(-459.81, 150)

Can you now calculate the distance and direction?