## BloomLocke367 one year ago Use the Law of Sines. Find m<C to the nearest tenth.

1. BloomLocke367

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2. sparrow2

m<c?

3. BloomLocke367

yes, the measure of angle C.

4. BloomLocke367

@Nnesha @perl @Preetha

5. sparrow2

so we need ti find sin24

6. BloomLocke367

but it's not a right triangle.

7. BloomLocke367

does that still apply?

8. BloomLocke367

I don't understand the Law of Sines

9. sparrow2

yes it still apply just write sin24

10. BloomLocke367

okay

11. BloomLocke367

I got 0.4067....

12. BloomLocke367

@sparrow2

13. sparrow2

so just enter this in the formula and then round nearest tenth

14. BloomLocke367

what formula?

15. BloomLocke367

@perl

16. sparrow2

law of sines

17. BloomLocke367

I don't know the formula.

18. sparrow2

162/sinc=77/sin24

19. sparrow2

then find sinc and look at the table to the relevant angle

20. BloomLocke367

what table? and I'm very confused right now..

21. sparrow2

values of trig function at different angle

22. perl

Does it make sense up to here $$\Large \frac{\sin 24^o}{77}= \frac{\sin C}{162}$$

23. BloomLocke367

why is it like that?

24. perl

here is a diagram of the law of sines http://www.mathworksheetsgo.com/sheets/trigonometry/advanced/law-of-sines-and-cosines/images/picture-law-of-sines-formula.jpg

25. BloomLocke367

ohhhh, yes that makes sense.

26. perl

so we are using just two parts of the three part ratio

27. perl

you can do that since they are equal

28. BloomLocke367

okay.

29. perl

we don't know sin B and b anyway at this point , yet

30. BloomLocke367

and we have to solve for C?

31. perl

$$\Large{ \frac{\sin 24^o}{77}= \frac{\sin C}{162} \\~\\ \iff \\~\\ \sin 24^o \times 162 = 77 \times \sin C \\~\\ \iff \\~\\ \frac{\sin 24^o \times 162}{77} = \sin C }$$

32. BloomLocke367

okay. and how do we isolate C?

33. perl

$$\Large{ \frac{\sin 24^o}{77}= \frac{\sin C}{162} \\~\\ \iff \\~\\ \sin 24^o \times 162 = 77 \times \sin C \\~\\ \iff \\~\\ \frac{\sin 24^o \times 162}{77} = \sin C \\~\\ \iff \\~\\ \sin^{-1} \left( \frac{\sin 24^o \times 162}{77} \right)= C }$$

34. BloomLocke367

that's what I thought, okay.

35. perl

make sure you are in degree mode if you are using a TI 83/84/85 calculator

36. BloomLocke367

I got 58.8

37. BloomLocke367

is that right?

38. perl

yes :)

39. perl

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40. BloomLocke367

Oh, wow. Thank you so much! I might need your help later, but I don't know. $$\Huge\rlap{\tt\color{teal}{Thank~you!}}{\;\tt\color{lime}{Thank~you!}}$$

41. perl

Now try to 'solve' the triangle (find all side lengths and angles). You can find angle B using the fact that three angles of any triangle add up to 180. Then use law of sines one more time to find side b, or alternatively you can use law of cosines

42. perl

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