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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)?

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  1. anonymous
    • one year ago
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  2. campbell_st
    • one year ago
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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

  3. anonymous
    • one year ago
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    150²+170²-2*150*170cos(139.17)° ?

  4. anonymous
    • one year ago
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    @campbell_st

  5. anonymous
    • one year ago
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    @freckles

  6. anonymous
    • one year ago
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    @Nnesha @jdoe0001

  7. jdoe0001
    • one year ago
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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

  8. anonymous
    • one year ago
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    150²+170²-2*150*170cos(139.17)° would this be the right way to input the values?

  9. jdoe0001
    • one year ago
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    yes just don't forget, you need to take the square root of that that is \(\bf \textit{Law of Cosines}\\ \quad \\ c^2 = {\color{blue}{ a}}^2+{\color{red}{ b}}^2-(2{\color{blue}{ a}}{\color{red}{ b}})cos(C)\\ \quad \\ c = \sqrt{{\color{blue}{ 150}}^2+{\color{red}{ 170}}^2-(2{\color{blue}{ 150}}\cdot {\color{red}{ 170}})cos(139.17^o)}\)

  10. anonymous
    • one year ago
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    would the answer be 226 miles?

  11. jdoe0001
    • one year ago
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    well \(\bf c = \sqrt{{\color{blue}{ 150}}^2+{\color{red}{ 170}}^2-(2\cdot {\color{blue}{ 150}}\cdot {\color{red}{ 170}})cos(139.17^o)}\)

  12. jdoe0001
    • one year ago
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    hmmm nope, is a bit more

  13. anonymous
    • one year ago
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    okay, ill recalculate

  14. jdoe0001
    • one year ago
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    well.. notice, the angle is in Degrees, thus, make sure when getting the cosine, your calculator is in Degree mode, as opposed to Radian

  15. anonymous
    • one year ago
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    i got a negative when i did cos(139.17)

  16. anonymous
    • one year ago
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    so it would be 300 miles?

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