## milliex51 3 years ago How do I find the measure of the indicated angle, to the nearest tenth of a degree using sine law and cosine law?

1. milliex51

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2. jiberjiber

Uh, what?

3. jiberjiber

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4. jiberjiber

four degrees?

5. milliex51

no, it's 104 degrees and the side length of BC is 45 m

6. Mertsj

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7. Mertsj

Let's say that side AB is c and use the law of cosines.

8. milliex51

|dw:1337046422125:dw| I found the side length of AC using cosine law: AC^2 = BC^2 + AB^2 - 2(BC)(AB)cosB = 45^2 + 20^2 - 2(45)(20)cos104 = 2860.459412 AC = 53.48 m

9. Mertsj

$c^2=20^2+45^2-2(20)(45)\cos 104$

10. milliex51

and then I used cosine law again to find the side length of DC: DC^2 = BC^2 _ BD^2 -2(BC)(BD)cosB = 45^2 + 30^2 -2(45)(30)cos(104 degrees) = 3578.19 I used the triangle BCD

11. milliex51

and now I am stuck..

12. Mertsj

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13. Mertsj

Now find the meassure of angle ACB using the law of sines.

14. Mertsj

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15. milliex51

but what angle am I suppose to find for triangle ABC, when angle B=104 degrees? wait I am confused..

16. Mertsj

$\frac{\sin 104}{53.48}=\frac{\sin ACB}{20}$

17. Mertsj

Angle ACB = 21.3 degrees

18. milliex51

how did you get 21.3?

19. milliex51

and the angle of C has to be 7.3 degrees..

20. Mertsj

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21. Mertsj

20(sin 104)/52.48 Then hit the inverse sin button.

22. milliex51

how did you get 54.7 and 21.3? :O i'm so sorry

23. Mertsj

Look above. It tells you how to get the 21.3. Then use the fact that the sum of the angles of a triangle is 180 to get 54.7

24. milliex51

ohh yup. But how am I going to find angle C? D:

25. Mertsj

But you want the angle theta so try this: $(CD)^2=30^2+45^2-2(30)(45)\cos 104$

26. Mertsj

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27. milliex51

i'm sorry but it just says, 'math processing error..'

28. Mertsj

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29. Mertsj

Now use the law of sines to find angle DCB. Subtract 21.3 from DCB and that will be theta.

30. milliex51

okay. I'm still kind of confused but thank you so much!

31. Mertsj

$\frac{\sin 104}{59.8}=\frac{\sin DCB}{30}$

32. Mertsj

33. milliex51

Mertsj, how come the answer at the back fo my book is 7.8 degrees? o.o

34. milliex51

ohh, never mind :\$ THANK YOU!!