An airplane leaves an airport and flies due west 150 miles and then 170 miles in the direction 210°50'. Assuming the Earth is flat, how far is the plane from the airport at this time (to the nearest mile)

Answer 1

150 at 180° = (-150,0)
170 at 210°50' = (-146,-87)

total: (-296,-87)

distance = √(296^2 + 87^2) = 309 mi

Answer 2

I am assuming that 0° is east. If you are using 0° = north, then things have to be changed a bit.