Posted by Brenden on .
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 straightline distance, how far is city C from city A? Relative to city A, in what direction is city C?

Physics 
MathMate,
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 = 18030=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?