Distance between plane and airport is 134.4 miles.
Given : An airplane leaves an airport and flies due west 150 miles and then 170 miles in the direction S 49.17°W.
To find : How far is the plane from the airport.
Solution : Distance from airport to west is 150 miles and then 170 miles in the direction south and angle form is S 49.17° W
Refer the attached picture for clearance.
Applying law of cosines
where a= 150 miles
C= 49.17° angle in degree
c = distance between plane from the airport
Put values in the formula,
Therefore, Distance between plane and airport is 134.4 miles.
I used the simplest geometry I could (wasn't sure what level of mathematics you were).
If the picture doesn't come through I'm sorry.
Final answer is 291.10936206249 miles or approximately 291 miles.
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