The brothers have a cousin Dewey who is a pilot, and who runs a crop dusting ser

Question

The brothers have a cousin Dewey who is a pilot, and who runs a crop dusting service.  One windy day, Dewey gives the brothers a ride in his crop dusting plane.  The brothers observe that they are flying due east, following the river, and by timing their passage over known landmarks along the riverbank, the boys are able to determine that their ground speed is 115 km/h.  Dewey doesn't have a working compass in the beat-up old plane, but he does have a working air speed indicator, and the boys observe that their air speed is 106 km/h.  The boys also observe that the plane is not pointed east, but rather somewhat south of east, and the weather report that they hear on Dewey's transistor radio tells them that the windspeed on this day is 24 km/h (but the report does not give the wind direction).  Cousin Dewey asks the boys to figure out the wind direction.  After some effort, the boys finally determine the wind direction by using the Law of Cosines.   Draw a proper velocity vector triangle for this case, and figure out how the boys were able to determine the wind direction.

What is the wind direction?  Give the direction as a positive angle of less than 90 degrees as measured from either East or West, and then indicate the proper way of expressing the direction.

Explanation / Answer

the direction is west and angle is 45 degree

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