anonymous one year ago Trig Sine and Cosine Law Am I correct? Please do not give answer but guide me. Thank you. Ok, I have a triangle with A= 60 degrees and two sides which are b = 12 and c = 17 Ok, this to me is a Side Angle Side problem SAS, which requires the Cosine Law. Ok to solve for $$a^2$$ we would use $$a^2 = b^2+c^2 -2\times b \times c \times cos A$$ which would be $$a^2 = 12^2+17^2 -2\times 12 \times 17 \times cos 60$$ which will equal $$a = \sqrt{229}$$ Ok, I have more to come but is that correct so far???

1. AbdullahM

Splendid work so far!

2. AbdullahM

You are on the correct path :) Now we have to use Law of Sines to calculate the rest.

3. anonymous

Ok now when I use $$cos B = \frac{\sqrt{229}^2+17^2}{2\times \sqrt{229}^2 \times 17}$$ I get an error on my calculator....

4. anonymous

Why can't I find B like the following

5. anonymous

Do we have to use Sine Law to find the rest. Why can't we use Cosine Law like the above?? My calculator errors out.

6. AbdullahM

Using the Sin Law would be more easier :)

7. Loser66

You apply cos b formula wrong

8. anonymous

But Cosine should work correct?but my two calculators give errors

9. Loser66

$$b^2 = a^2+c^2 -2ac cosb\\2ac cosb= a^2+c^2 -b^2\\cosb=\dfrac{a^2+c^2-b^2}{2ac}$$

10. anonymous

Ah crap Loser66 you are right lol I forgot the -b^2 Man I thought I was losing my mind. I was like it should work LOL

11. anonymous

Thanks to you all.

12. anonymous

Still getting an error. Grrrrr lol

13. Loser66

why? what do you hit on your calculator? , You need $$\angle b$$ right?

14. anonymous

Going to try my Ti nspire cx Still getting error on my Casio fx 115

15. Loser66

My calculator said that b is $$\approx 41^0$$

16. anonymous

Crap, I see where I made my mistake. I need to slow down. I hite times instead of plus

17. anonymous

I got 43.37 degreess

18. Loser66

hihihi... now, do it together: a^2 +c^2 -b^2 = 299 +17^2 -12^2 =444 ok?

19. AbdullahM

I got 43.47 also

20. Loser66

now divided by (2*17*sqrt (299) , we get 0.7552112641 ok?

21. anonymous

Cool, thanks Loser66 and AbdullahM, Sending you both 5 owlbucks. Thanks for the help

22. anonymous

I got it from here.

23. AbdullahM

Anytime :))

24. Loser66

now hit "2nd + cos^-1" then type 0.7552112641 it gives us 40.97463023

25. Loser66

hihihi... that's what my calculator said.

26. AbdullahM

Just to make sure, we can plug it into a calculator.

27. AbdullahM
28. Loser66

sorry for correcting you again $$a=\sqrt{299}= 17.29$$ not 15.13.. as you stated

29. AbdullahM

Her number is $$\bf 229$$ not 299.

30. Loser66

oh yeah. my bad. I was wrong.