An airplane has an airspeed of 540 mph at a bearing of 80 degrees. The wind velocity is 55 mph with a 100 degree bearing . Find the resultant speed and the bearing of the airplane.

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Danny -The airplane airspeed vector is:540[ cos(80)i + sin(80)j ]Once The wind velocity vector is:55[ cos(100)i + sin(100)j ]The resultant vector is simply the SUM of the airspeed and velocity vectors above.Once you determine the "resultant vector", the resultant speed is simply the square root of the sum of the i & j components squared.The bearing must be between 80 and 100 degrees, agree?  Also, remember bearing is defined relative to true north, so for example 90 degrees is due east.  So, use the tangent formula, but adjust for the fact this is a bearing and not an angle from the unit circle.Hope that helps