Question

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???

Answer 1

Splendid work so far!

Answer 2

You are on the correct path :)

Now we have to use Law of Sines to calculate the rest.

Answer 3

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....

Answer 4

Why can't I find B like the following

Answer 5

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.

Answer 6

Using the Sin Law would be more easier :)

Answer 7

You apply cos b formula wrong

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

Thanks to you all.

Answer 12

Still getting an error. Grrrrr lol

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

I got 43.37 degreess

Answer 18

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

Answer 19

I got 43.47 also

Answer 20

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

Answer 21

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

Answer 22

I got it from here.

Answer 23

Anytime :))

Answer 24

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

Answer 25

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

Answer 26

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

Answer 27

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

Answer 28

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

Answer 29

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

Answer 30

oh yeah. my bad. I was wrong.