A pilot wants the heading of an airplane to be 45º east of north. The wind is from 270º at 32 km/h, and the speed of the airplane through the air is 320 km/h. The pilot should maintain a heading of approximately?

Answer 1

we want our east component to equal our north component so we get 45 degrees resultant. Wind is FROM 270, west.

Heading or compass direction is clockwise from North

wind is going 90 or East
so our East speed is 320 sin(heading) + 32
and our north component is 320 cos (heading)
so
320 sin heading + 32 = 320 cos heading

sin heading + 0.1 = cos heading

try some guesses

heading = 10 deg
left =.17+.1 = .27
right = .98
heading = 20 deg
left = .34+.1 =.44
right = .93
heading = 30 deg
left = .6
right = .86
heading = 40 deg
left = .74
right .76 really close !
heading = 42 deg
left = .77
right= .74
so between 40 and 42,
heading = 41 deg
left = .756
right = .754
Steer a compass heading of N 41 E