Question

How do you use law of sines to solve the triangle given A=43 degrees, a= 6.3, c=2.5?

Answer 1

Step 1: `=> sin(C)=c/a*sin(A)=s`
Step 2: `C = arcsin(s)` or `C=180^o-arcsin(s)`
Step 3: `B=180^o-A-C`
Step 4: `=> b=a*sin(A)/sin(B)`

Explanation:

The Law of Sines states that in triangle `Delta ABC` the following equation between angles and sides is true:
`a/sin(A) = b/sin(B) = c/sin(C)`

If `a` and `c` are known sides and `A` is a known angle, we can determine angle C from
`a/sin(A) = c/sin(C)`
`=> sin(C)=c/a*sin(A)`
This is supposed to be used to find angle `C` by its `sin(C)`. In theory, there might be two different values for angle `C` and both should be carefully examined on validity.

Since we have determined angle `C`, we can determine angle `B` using the fact that `A+B+C=180^o`:
`=>B = 180^o-A-C`

Now, knowing angle B, we can determine side `b` from
`a/sin(A)=b/sin(B)`
`=> b=a*sin(A)/sin(B)`

We leave numerical calculations as self-study exercise.