Answer:
about 2.9° north of east
Step-by-step explanation:
If we orient the directions so north is in the +y direction and east is in the +x direction, the car is traveling 13 km at an angle of -45°, then 16 km at an angle of +40°. We can add these vectors by adding their components in the x- and y-directions.
13(cos(-45°), sin(-45°)) ≈ (9.19239, -9.19239)
16(cos(40°), sin(40°)) ≈ (12.25671, 10.28460)
The sum of these vectors is then ...
= (21.44910, 1.09221)
and the resultant angle is ...
arctan(1.09221/21.44910) ≈ 2.915° . . . . measured north of east
The resultant direction is about 2.9° north of east.
