We will see that the plane must travel at 44° north of east.
How to find the direction?
If the airplane travels with an angle θ measured north from east, the components of the velocity will be:
- East component = (580 km/h)*cos(θ)
- North component = (580km/h)*sin(θ)
If we also add the wind, that flows from north, the components of the plane's velocity will be:
- East component = (580 km/h)*cos(θ)
- North component = (580km/h)*sin(θ) - 82 km/h
Now we want our plane to travel 38° north of east, if you see this like a right triangle, then we must have:
Tan(38°) = (north component)/(east component)
0.78 = tan(θ) - (82/580)*(1/cos(θ))
0.78 = tan(θ) - (0.14/cos(θ))
This must be solved graphically, and the graph of the equation is shown below, there, you can see that the first root is x = 0.773
This is in radians, remember that:
3.14 rad = 180°
Then:
0.773 rad = (0.773/3.14)*180° = 44°
This means that the plane must fly at 44° north of east.
If you want to learn more about directions, you can read:
https://brainly.com/question/2246270
