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anonymous

  • one year ago

Triangle LMN has vertexes at L(-1, -6), M(1, -6), and N(1, 1). Find the measure of angle L to the nearest degree. (Hint: Sketch the triangle on the coordinate plane and find the side lengths using the Distance Formula first.)

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  1. DanJS
    • one year ago
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    k

  2. anonymous
    • one year ago
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    I found the other length for LN and it would be 7.28

  3. anonymous
    • one year ago
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    MN is 7 and LM is 2.

  4. DanJS
    • one year ago
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    |dw:1441238664615:dw|

  5. jdoe0001
    • one year ago
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    ok yes, I'd say, get the segment's length first, then use the law of cosines \(\bf \cfrac{{\color{blue}{ a}}^2+{\color{red}{ b}}^2-c^2}{2{\color{blue}{ a}}{\color{red}{ b}}}=cos(C)\implies cos^{-1}\left(\cfrac{{\color{blue}{ a}}^2+{\color{red}{ b}}^2-c^2}{2{\color{blue}{ a}}{\color{red}{ b}}}\right)=\measuredangle C\)

  6. DanJS
    • one year ago
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    I think you miscalculated the LM side length, it is for sure larger than 2

  7. anonymous
    • one year ago
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    How would it not be 2. Like i did the distance formula and used the graph and its 2 lol

  8. DanJS
    • one year ago
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    sorry, i see

  9. DanJS
    • one year ago
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    |dw:1441239106211:dw|

  10. DanJS
    • one year ago
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    my mistake

  11. DanJS
    • one year ago
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    so you have... |dw:1441239177811:dw|

  12. anonymous
    • one year ago
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    and 7.28

  13. DanJS
    • one year ago
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    it is actually a right triangle,

  14. anonymous
    • one year ago
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    yes

  15. DanJS
    • one year ago
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    MN is vertical, have same x coordinate and LM is horizontal with the same y coordinate

  16. DanJS
    • one year ago
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    you can use whichever trig function now since it is a right triangle

  17. DanJS
    • one year ago
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    tangent of L is the opposite side over the adjacent side

  18. DanJS
    • one year ago
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    Tan(L) = 7/2

  19. DanJS
    • one year ago
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    it was actually pretty easy, no law of cosines to calculate...just my plotting points wrong to start

  20. anonymous
    • one year ago
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    But how do you get L?

  21. DanJS
    • one year ago
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    have you used the arctangent function? tan^(-1) ...usually 2nd or shift and tangent on the calculator

  22. anonymous
    • one year ago
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    so it'd be 74.1?

  23. DanJS
    • one year ago
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    looks about right

  24. anonymous
    • one year ago
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    And N would be 16?

  25. DanJS
    • one year ago
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    tan^(-1)(7/2) =

  26. DanJS
    • one year ago
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    yeah the three angles total 180

  27. anonymous
    • one year ago
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    Thanks !

  28. DanJS
    • one year ago
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    no prob, welcome

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