A car is driving east for a distance of 50km, then north for 30km and then in a direction 30 east of north for 25km. Determine the angle of the car's total displacement from its starting point?
Break each vector component into its constituent parts (N/S & E/W), then add them all. Vector 3 needs a trigonometry calculation.
Vector 1: 0 km North/South, 50 km East/West
Vector 2: 30 km North/South, 0 km East/West
Vector 3: cos 30 x 25 = 21.65 km N/S, sin 30 x 25 = 12.5 km E/W
The sums: 51.65 km N/S, 62.5 km E/W
Using trigonometry again, tan = opp./adj. = 62.5km/51.65km = 1.21
Turning this into an angle, you get 50.4 degrees East of North