An airplane is traveling at a speed of 240 miles/hour with a bearing of 110°. The wind velocity is 56 miles/hour at a bearing of 325°. What are the plane's actual speed and direction angle?

Answer:Actual speed = 288 miles per hourActual direction angle = [tex]116.38^\circ[/tex]Step-by-step explanation:"Bearing" is the relative position of an object outside the plane compared to the position of the plane.  Heading the the direction the nose of the plane is pointing.  Course is the direction that pilot wants the plane to go.  Wind direction is always the direction the wind is blowing from.  The airplane is traveling at a speed of 240 miles/hour with a bearing of 110°.  If the plane is traveling with a bearing of 110° and the wind is blown at a bearing of 325°.    [tex]325^{\circ}- 110^{\circ} =225^{\circ}[/tex][tex]215^{\circ}- 180^{\circ} =35^{\circ}[/tex]The Ground speed will be in excess of the airspeed and true direction will be south if the indicated heading.  The tailwind component is: [tex]56 cos (35^\circ)[/tex]And the cross wind component is: [tex]56 sin (35^\circ)[/tex]  
And that is,[tex]C^2 = (286)^2 + (32)^2[/tex]
[tex]c = 288[/tex]So the actual speed of the plane is 288 miles per hour. The deviation in the direction is:Let the direction angle be 'x'. [tex]x = tan ^{-1}\left ( \frac{32}{286} \right )=6.38^\circ[/tex]So the actual direction angle is [tex]110^\circ+ 6.38^\circ=116.38^\circ[/tex].