About Law of Cosines and Law of Sines?

Question

Im Solving a word problem that only has the three sides of the triangle and Im using law of cosines to find the angle of one side, is it possible for me to use law of sines after that? or do I hafta continue using law of cosines?

Ex: Side a=153
Side b= 175
Side c= 201

I just found the measure of angle A through the law of cosines and it is: 47.405 degrees

So can i use law of sines? or do i continue using law of cosines?

Answer 1

Cosine Rule
a² = b² + c² - 2b cos A
So angle A be be calculated

b² = a² + c² - 2ac cos B
So angle B may be calculated.

A + B + C = 180
Thus angle C may be found.

A, B and C are now known.
a , b and are given.

Sine Rule
a/ sin A = b/sin B = c / sin C

After A was found (cosine rule) could use
a/sin A = b / sin B to find B

Can then find C as A + B + C = 180

Answer 2

Nomenclature: angle C is the angle across from side c on the triangle ABC. Sine law works for all triangles; a/sin A = b/sin B = c/sin C. Unless you admit the possibility of true zero-angle triangles; the law is invalid for that case. Cosine law works for all triangles, as well. a^2 + b^2 - 2 a*b*cos C = c^2 Some rules might require special conditions, but none of them simply state that the triangle cannot have a right angle. As far as I know, these two laws have no special exceptions.

Answer 3

After finding angle A using law of cosines, you can find angla B, either using law of cosines again or law of sines:
sinB/b=sinA/a.
Finally you can find angle C:
C=180-(A+B).

Answer 4

Unless you are told that you should the law of cosines, it wouldn't matter what method you used as long as you got the answer.

Answer 5

Yes, of course you can. Once yo know one angle you can use either law. The law of sines is quicker.

Answer 6

Yes u ca use the law of sines.

Answer 7

you can use law of sines if you want