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anonymous
 one year ago
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)?
anonymous
 one year ago
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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campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0the 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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0150²+170²2*150*170cos(139.17)° ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0actually, as @cambell_st is correct the angle shown there, is just a portion of the 90 degreesdw:1441064992008:dw and you can use the law of cosines to find the missing side, or distance to the airport

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0150²+170²2*150*170cos(139.17)° would this be the right way to input the values?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes just don't forget, you need to take the square root of that that is \(\bf \textit{Law of Cosines}\\ \quad \\ c^2 = {\color{blue}{ a}}^2+{\color{red}{ b}}^2(2{\color{blue}{ a}}{\color{red}{ b}})cos(C)\\ \quad \\ c = \sqrt{{\color{blue}{ 150}}^2+{\color{red}{ 170}}^2(2{\color{blue}{ 150}}\cdot {\color{red}{ 170}})cos(139.17^o)}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0would the answer be 226 miles?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0well \(\bf c = \sqrt{{\color{blue}{ 150}}^2+{\color{red}{ 170}}^2(2\cdot {\color{blue}{ 150}}\cdot {\color{red}{ 170}})cos(139.17^o)}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hmmm nope, is a bit more

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay, ill recalculate

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0well.. notice, the angle is in Degrees, thus, make sure when getting the cosine, your calculator is in Degree mode, as opposed to Radian

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i got a negative when i did cos(139.17)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so it would be 300 miles?
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