Posted by **Jon** on Friday, March 7, 2008 at 1:38pm.

Should the triangle be solved beginning with Law of Sines of Law of Cosines. Then solve the triangle. Round to the nearest tenth. A=56 degrees, B=38 degrees, a=13.

Sines. I get confused on the formula. I know C=86 degrees

- Trig -
**Reiny**, Friday, March 7, 2008 at 2:18pm
To solve a triangle you must be given 3 independent bits of information.

2 sides and 1 angle

3 sides

1 side and 2 angles

(note 3 angles is not "3 independent pieces of information, since if you know 2 angles, you automatically know the third)

general simple rule:

If you are given a side and its opposite angle, use the sine law

if not, use cosine law.

so for yours, clearly sine law.

- Trig(I know all of that I just need to know how to use the formula) -
**Jon**, Friday, March 7, 2008 at 2:47pm
I know I need to use the law of sines but I don't really know how and which one to use like sinA/a= sin B/b and sinB/b =sinC/c and sinA/a = sinC/c. That's where I get confused.

- Trig -
**Reiny**, Friday, March 7, 2008 at 2:56pm
clearly you are given a side and its opposite angle, a and A, so that is obviously the ratio you are going to use

SinA/a = SinB/b

sin56/13 = sin38/b crossmultiply and solve for b.

b = 13sin38/sin56

= 9.65

do the same to find c

- Trig -
**Jon**, Friday, March 7, 2008 at 3:23pm
b=9.7(i had to round)

im not sure if im doing this right.

SinB/b = SinC/c

Sin38/9.7 = Sin86/c

c = 9.7sin38/sin86

c= 5.98 or 6 since I have to round to nearest tenth.

- Trig -
**Reiny**, Friday, March 7, 2008 at 3:30pm
why would you not stick with the exact ration sin56/13, which uses the original numbers given

You used an answer that you obtained after you rounded off that answer, so you are compounding your error.

- Trig -
**Jon**, Friday, March 7, 2008 at 3:36pm
so to find c all I have to do is

Sin56/13 = Sin86/c

c = 13Sin56/Sin86

c = 10.8

- Trig -
**Reiny**, Friday, March 7, 2008 at 3:50pm
NO

Sin56/13 = Sin86/c now cross-multiply

csin56 = 13sin86 divide by sin56

c = 13sin86/sin56

c = 15.6

check: in any triangle, your smallest side should be across from the smallest angle, the largest side should be across the largest angle.

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