# Jim says that the sine law cannot be used to determine the length of side c in at the left. Do you agree or disagree? Explain.? Relevance
• Disagree. We can use the sine law to detemine the length of side c.

But it becomes complicated.

By the sine law,

3/sinA = 3.2/sinB

And we know

B = 180° - (70° + A) = 110° - A

So

3/sinA = 3.2/sin(110° - A)

3sin(110° - A) = 3.2sinA

3sin110°cosA - 3cos110°sinA = 3.2sinA

3sin110°cosA = (3cos110° + 3.2)sinA

3sin110°/(3cos110° + 3.2) = sinA/cosA

1.296... = tanA

A = 52.36° (approx.)

By the sine law again,

c/sin70° = 3/sinA

c = 3sin70°/sinA

c = 3.56 (approx.)

Clearly the cosine law is suitable for this problem.

c^2 = 3^2 + 3.2^2 - 2*3*3.2*cos70°

c^2 = 12.67...

c = 3.56 (approx.)

• Agree.   Law of Sines:   SinA/a = SinB/b = SinC/c

You don't have enough information to use Law of Sines.

You need to use the law of Cosines to solve your triangle.

Two Sides and the Angle between them.

c^2 = a^2 + b^2 - 2ab(cos(C)

c^2 = 9 +  10.24 - 6.5668

c=3.5

• The Sine Law requires you have one angle and the opposite side defined. Then for any other provided angle, you can find the opposite side. (Or for any other provided side, you can find the opposite angle).

If you knew angle A, or angle B, then you could use the Law of Sines, but as set up, you cannot.

Fortunately, in this scenario you can just switch to the Law of Cosines to figure out the opposite side.