Problem: A pilot wishes to fly from Bayfield to London, a distance of 85 km on a bearing of 160°. The speed of the plane in still air is 250 km/h. A 20 km/h wind is blowing on a bearing of 030°.
Remembering that she must fly on a bearing of 160° relative to the ground (ie the resultant must be on that bearing),
-
find the heading she should take to reach her destination.
-
how long the trip will take.
Have I illustrated this problem correctly? problem
How do I find the angle between the planes desired heading and the wind?
Best Answer
If $030$ is the direction the wind is coming from, then your diagram is correct. I've certainly seen wind direction interpreted this way in the aviation field, but I'm not altogether certain what the person posing this problem thought the direction meant. The alternative interpretation is that the wind is blowing from $210$ toward $030$.
Assuming the wind direction is "from $030$", you can divide your wind triangle into two right triangles by dropping a perpendicular from the rightmost vertex to the $160^\circ$ course. This gives you one right triangle with an angle of $50^\circ$ adjacent to the course and a hypotenuse of $20$. The length of the perpendicular that you dropped is therefore $20\, \sin(50^\circ)$. The other triangle has a hypotenuse of $250$.
So now you know the hypotenuse and one leg of each of your two right triangles. From this you can find all the angles (including the one between the aircraft's heading and course $160$), and you can find the lengths of the other legs of the triangle, which together add up to the length of the velocity vector along course $160$. So now you know the speed of the aircraft relative to the ground, and you can compute the time to travel $85$ km.