Question 144131: An airplane heads N 35 degrees W at an airspeed of 350 miles per hour with a wind blowing from the east at 19 miles per hour. Approximate the ground speed of the plane to the nearest mile per hour and determine the actual direction of the flight to the nearest degree.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Draw a line from the origin heading 325 degrees (35 degs) left of vertical. This represents the speed and direction of the plane. Label the length 325, the speed, with an arrow on the far end (not at the origin).
From the end on that line, draw a line horizontal. This represents the wind speed. Label its length 19, and put an arrow on its end.
Draw a line from the origin to the arrowhead on the line 19 mph long. This line is the path of the plane, and its length is the groundspeed of the plane.
Solve for the length of this line, and for the angle between the 2 lines at the origin.
Find the angle:
The angle between the 325 line and the x-axis is 90-35, or 55 degs. Since the 19 line is parallel to the x-axis, the angle INSIDE the triangle is 180-55, or 125 degs.
Now we know 2 sides and the included angle, so we can find the 3rd side using the law of cosines.
c = 336.26 mph
The law of sines is quicker than doing the law of cosines again.
336.26/sin(125) = 19/sin(O) (O = angle at the origin)
sin(O) = 19sin(125)/336.26
sin(O) = 0.04628
O = 2.653 degrees CCW of the heading, which is a heading of 322.35 degrees, or 37.65 degs West of North. The groundspeed is 336 mph.
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