Question

A car is driven 225km west and then 98 km southwest (45∘). What is the displacement of the car from the point of origin (magnitude)?

Answer 1

We will use the Cosine rule ( graph is in the attachment ):
c - the displacement
Angle: 90° + 45° = 135°
c² = a² + b² - 2 ab cos 135° 
c² = 98² + 225² - 2 · 98 · 225 · ( -0.7071 ) 
c² = 9,604 + 50,625 + 31,183.11
c² = 91,412.11
c = √ 91,412.11
c = 302.344 km