An airplane leaves an airport and flies due west 150 miles and then 170 miles in the direction S 49.17°W. How far is the plane from the airport (round to the nearest mile)?

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An airplane leaves an airport and flies due west 150 miles and then 170 miles in the direction S 49.17°W. How far is the plane from the airport (round to the nearest mile)?

Mathematics
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the angle that includes the angle is 90 + 49.17 = 139.17 so then you can use the law of cosines to find the distance Plane to Airport
150²+170²-2*150*170cos(139.17)° ?

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actually, as @cambell_st is correct the angle shown there, is just a portion of the 90 degrees|dw:1441064992008:dw| and you can use the law of cosines to find the missing side, or distance to the airport
150²+170²-2*150*170cos(139.17)° would this be the right way to input the values?
yes just don't forget, you need to take the square root of that that is \(\bf \textit{Law of Cosines}\\ \quad \\ c^2 = {\color{blue}{ a}}^2+{\color{red}{ b}}^2-(2{\color{blue}{ a}}{\color{red}{ b}})cos(C)\\ \quad \\ c = \sqrt{{\color{blue}{ 150}}^2+{\color{red}{ 170}}^2-(2{\color{blue}{ 150}}\cdot {\color{red}{ 170}})cos(139.17^o)}\)
would the answer be 226 miles?
well \(\bf c = \sqrt{{\color{blue}{ 150}}^2+{\color{red}{ 170}}^2-(2\cdot {\color{blue}{ 150}}\cdot {\color{red}{ 170}})cos(139.17^o)}\)
hmmm nope, is a bit more
okay, ill recalculate
well.. notice, the angle is in Degrees, thus, make sure when getting the cosine, your calculator is in Degree mode, as opposed to Radian
https://www.google.com/search?client=opera&q=sqrt(150%5E2%2B170%5E2-2*150*170*cos(139.17+degrees))&sourceid=opera&ie=utf-8&oe=utf-8&channel=suggest&gws_rd=ssl
i got a negative when i did cos(139.17)
so it would be 300 miles?

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