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???

- anonymous

- jamiebookeater

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- AbdullahM

Splendid work so far!

- AbdullahM

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

- 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....

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## More answers

- anonymous

Why can't I find B like the following

- 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.

- AbdullahM

Using the Sin Law would be more easier :)

- Loser66

You apply cos b formula wrong

- anonymous

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

- Loser66

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

- 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

- anonymous

Thanks to you all.

- anonymous

Still getting an error. Grrrrr lol

- Loser66

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

- anonymous

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

- Loser66

My calculator said that b is \(\approx 41^0\)

- anonymous

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

- anonymous

I got 43.37 degreess

- Loser66

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

- AbdullahM

I got 43.47 also

- Loser66

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

- anonymous

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

- anonymous

I got it from here.

- AbdullahM

Anytime :))

- Loser66

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

- Loser66

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

- AbdullahM

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

- AbdullahM

http://www.mathwarehouse.com/triangle-calculator/online.php?&sb=12&sc=17&aa=60#triangleAppData

- Loser66

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

- AbdullahM

Her number is \(\bf 229\) not 299.

- Loser66

oh yeah. my bad. I was wrong.

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