Step-by-step explanation:
the displacement is the length of direct line of sight from the starting point to the end point. in other word the baseline of the created triangle.
the legs of that triangle are 10 cm and 6 cm.
the angle between both legs is 90 + 45 = 135°.
because 90° is the angle between South and West. and for southwest we have to add 45°
the law of cosine :
c² = a² + b² - 2ab×cos(C)
c is a side, C is the opposite angle, a and b are the other 2 sides.
so, we have in our case
displacement² = 10² + 6² - 2×10×6×cos(135) =
= 100 + 36 - 120×cos(135) =
= 136 - 120×-0.707106781... =
= 136 - 120×-sqrt(2)/2 =
= 136 + 60×sqrt(2) =
= 220.8528137...
displacement = 14.86111751... cm ≈ 15 cm