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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

k

2. anonymous

I found the other length for LN and it would be 7.28

3. anonymous

MN is 7 and LM is 2.

4. DanJS

|dw:1441238664615:dw|

5. anonymous

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

I think you miscalculated the LM side length, it is for sure larger than 2

7. anonymous

How would it not be 2. Like i did the distance formula and used the graph and its 2 lol

8. DanJS

sorry, i see

9. DanJS

|dw:1441239106211:dw|

10. DanJS

my mistake

11. DanJS

so you have... |dw:1441239177811:dw|

12. anonymous

and 7.28

13. DanJS

it is actually a right triangle,

14. anonymous

yes

15. DanJS

MN is vertical, have same x coordinate and LM is horizontal with the same y coordinate

16. DanJS

you can use whichever trig function now since it is a right triangle

17. DanJS

tangent of L is the opposite side over the adjacent side

18. DanJS

Tan(L) = 7/2

19. DanJS

it was actually pretty easy, no law of cosines to calculate...just my plotting points wrong to start

20. anonymous

But how do you get L?

21. DanJS

have you used the arctangent function? tan^(-1) ...usually 2nd or shift and tangent on the calculator

22. anonymous

so it'd be 74.1?

23. DanJS

looks about right

24. anonymous

And N would be 16?

25. DanJS

tan^(-1)(7/2) =

26. DanJS

yeah the three angles total 180

27. anonymous

Thanks !

28. DanJS

no prob, welcome

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