An airplane's velocity with no wind is 580km/h with a bearing of N 60 Degrees.

Question

The wind has a velocity 60km/h and is blowing S 45 degrees E. What is the true speed and bearing of the plane?

Answer 1

N 60 E (I assume) at 580
N component = 580 cos 60 =290 km/h
E component = 580 sin 60 = 502 km/h
now I assume you mean it is blowing TOWARD S 34 E
( in navigation we usually state wind direction FROM but we also say "heading" not "bearing" unless we are taking a bearing so I assume a non-navigator wrote the question)
wind drift S = 60 *.707 = 42.4 km/h
wind drift E = 60 *.707 = 42.4 km/h
total speed N = 290 - 42.4 = 248
total speed E = 503 + 42.4 = 545
speed = sqrt(248^2 + 545^2)
tan angle East of North = 545 / 248