Trigonometry: plane, wind speed and wind direction?

I'm not understanding this question too well and have drawn it below as I've visualized it (not drawn to scale).

If a plane is travelling due north 320 degrees with an air speed of 300 km/h, and has a track (drift?) of 325 degrees and ground speed 280 km/h, work out the speed of the wind and its direction.

I have the speed at 35 km/h, and the direction is 271 degrees due north, whereas the answer is 89 degrees. I can see that this is the part of the upper circle that's missing, but I can't understand why its 89 rather than 271. 


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1 Answer

  • 1 month ago

    You are missing the arrows. These are vital. We know that the speed of the plane relative to the air + speed of the air relative to the ground gives the speed of the plane relative to the ground.

    So the vector at 320 degrees needs its arrow at the top.  The vector of the air must START from this point and have its arrow at the far end ( the top of the 325 degree vector.

    The RESULTANT must start from the beginning of the 325 degree vector and end at the end of the wind vector.  That means that the wind must be pointing generally east  Hence 89 is possible.  Although I haven't bothered to check the exact number.  But 271 is impossible if the arrows are drawn properly.

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