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.

Question

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

Answer 1

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.

Answer 2

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.

Answer 3

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

Answer 4

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.

Answer 5

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.

Answer 6

so to find c all I have to do is

Sin56/13 = Sin86/c
c = 13Sin56/Sin86
c = 10.8

Answer 7

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.