Question

An aeroplane flies 520 km north 45 degrees west then 387 km east . it is then noted that the plane is due north of its starting point. how far is the plane from its starting point?

How do I work it out?

Answer 1

Hope you made a sketch.
In mine I can use the cosine law

let the distance from the starting point be x
x^2 = 520^2 + 387^2 - 2(520)(387)cos45°
= 135572.6627
x = √....
= 368.2 km

Answer 2

a^2= 520^2-387^2
a^2= 270400-149769
a^2= 120631
a=347.32