Answer:
Distance between plane and airport is 134.4 miles.
Step-by-step explanation:
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
![c^2=a^2+b^2-2ab Cos(C)](https://tex.z-dn.net/?f=c%5E2%3Da%5E2%2Bb%5E2-2ab%20Cos%28C%29)
![c=\sqrt{a^2+b^2-2ab Cos(C)}](https://tex.z-dn.net/?f=c%3D%5Csqrt%7Ba%5E2%2Bb%5E2-2ab%20Cos%28C%29%7D)
where a= 150 miles
b=170 miles
C= 49.17° angle in degree
c = distance between plane from the airport
Put values in the formula,
![c=\sqrt{a^2+b^2-2ab Cos(C)}](https://tex.z-dn.net/?f=c%3D%5Csqrt%7Ba%5E2%2Bb%5E2-2ab%20Cos%28C%29%7D)
![c=\sqrt{150^2+170^2-2(150)(170) Cos(49.17^{\circ})}](https://tex.z-dn.net/?f=c%3D%5Csqrt%7B150%5E2%2B170%5E2-2%28150%29%28170%29%20Cos%2849.17%5E%7B%5Ccirc%7D%29%7D)
![c=\sqrt{22500+28900-51000(0.653)}](https://tex.z-dn.net/?f=c%3D%5Csqrt%7B22500%2B28900-51000%280.653%29%7D)
![c=\sqrt{51400-33303}](https://tex.z-dn.net/?f=c%3D%5Csqrt%7B51400-33303%7D)
![c=\sqrt{18057}](https://tex.z-dn.net/?f=c%3D%5Csqrt%7B18057%7D)
![c=134.37](https://tex.z-dn.net/?f=c%3D134.37)
Therefore, Distance between plane and airport is 134.4 miles.