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Finding the resultant speed of a plane

A plane is heading due north with a ground speed of 405 mph. A 30 mph wind is blowing at a bearing of 48degrees. find the planes resulting speed.

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W ewill apply the law of sines and the law of Cosines to solve this. Please see the attached figure.

The angle theta is the difference between wind direction and the desired bearing. With that angle and the law of sines, the offset angle beta for the ...

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Clear explanations and all mathematical steps are provided.