anonymous
  • anonymous
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
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
1 Attachment
campbell_st
  • campbell_st
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
anonymous
  • anonymous
150²+170²-2*150*170cos(139.17)° ?

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anonymous
  • anonymous
@campbell_st
anonymous
  • anonymous
@freckles
anonymous
  • anonymous
@Nnesha @jdoe0001
jdoe0001
  • jdoe0001
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
anonymous
  • anonymous
150²+170²-2*150*170cos(139.17)° would this be the right way to input the values?
jdoe0001
  • jdoe0001
yes just don't forget, you need to take the square root of that that is \(\bf \textit{Law of Cosines}\\ \quad \\ c^2 = {\color{blue}{ a}}^2+{\color{red}{ b}}^2-(2{\color{blue}{ a}}{\color{red}{ b}})cos(C)\\ \quad \\ c = \sqrt{{\color{blue}{ 150}}^2+{\color{red}{ 170}}^2-(2{\color{blue}{ 150}}\cdot {\color{red}{ 170}})cos(139.17^o)}\)
anonymous
  • anonymous
would the answer be 226 miles?
jdoe0001
  • jdoe0001
well \(\bf c = \sqrt{{\color{blue}{ 150}}^2+{\color{red}{ 170}}^2-(2\cdot {\color{blue}{ 150}}\cdot {\color{red}{ 170}})cos(139.17^o)}\)
jdoe0001
  • jdoe0001
hmmm nope, is a bit more
anonymous
  • anonymous
okay, ill recalculate
jdoe0001
  • jdoe0001
well.. notice, the angle is in Degrees, thus, make sure when getting the cosine, your calculator is in Degree mode, as opposed to Radian
jdoe0001
  • jdoe0001
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
anonymous
  • anonymous
i got a negative when i did cos(139.17)
anonymous
  • anonymous
so it would be 300 miles?

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