Mathematicians should not write navigation problems:
an airplane has an airspeed of 430 miles per hour ***ON*** a ****HEADING**** of 135 degrees. the wind velocity is 35 miles per hour in the direction N30degreesE. Find the resultant speed and direction of the plane.
Usually we say where the wind is FROM but this seems to imply that the air is moving N 30 E . Again mathematicians do not get this stuff.
North speed = 430 cos 135 + 35 cos 30
= -273 mph or 273 south
East speed = 430 sin 135 + 35 sin 30
= 322 mph
total speed = sqrt(273^2+322^2) = 422 mph
angle of travel east of south = A
tan A = 322/273
A = 49.7
so actual direction over ground is
180 - 49.7 = 130.3 degrees East of North