milliex51 Group Title How do I find the measure of the indicated angle, to the nearest tenth of a degree using sine law and cosine law? 2 years ago 2 years ago

1. milliex51 Group Title

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2. jiberjiber Group Title

Uh, what?

3. jiberjiber Group Title

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4. jiberjiber Group Title

four degrees?

5. milliex51 Group Title

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

6. Mertsj Group Title

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7. Mertsj Group Title

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

8. milliex51 Group Title

|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 Group Title

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

10. milliex51 Group Title

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 Group Title

and now I am stuck..

12. Mertsj Group Title

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13. Mertsj Group Title

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

14. Mertsj Group Title

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15. milliex51 Group Title

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

16. Mertsj Group Title

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

17. Mertsj Group Title

Angle ACB = 21.3 degrees

18. milliex51 Group Title

how did you get 21.3?

19. milliex51 Group Title

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

20. Mertsj Group Title

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21. Mertsj Group Title

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

22. milliex51 Group Title

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

23. Mertsj Group Title

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 Group Title

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

25. Mertsj Group Title

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

26. Mertsj Group Title

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27. milliex51 Group Title

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

28. Mertsj Group Title

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29. Mertsj Group Title

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

30. milliex51 Group Title

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

31. Mertsj Group Title

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

32. Mertsj Group Title