Question

If ∠R is given and the values of r and q are given, then explain whether the Law of Sines or the Law of Cosines should be used to solve for ∠Q.

Answer 1

To solve a triangle is to find the lengths of each of its sides and all its angles. The sine rule is used when we are given either a) two angles and one side, or b) two sides and a non-included angle. The cosine rule is used when we are given either a) three sides or b) two sides and the included angle.

Explanation:

We just saw how to find an angle when we know three sides. It took quite a few steps, so it is easier to use the "direct" formula (which is just a rearrangement of the c2 = a2 + b2 − 2ab cos(C) formula). It can be in either of these forms:

cos(C) = a2 + b2 − c22ab

cos(A) = b2 + c2 − a22bc

cos(B) = c2 + a2 − b22ca

Answer 2

Law of cosines, two sides and the included angle known

Explanation:

double check that the question is exactly the same to make sure you get the question correct

"If ∠P is given and the values of r and q are given, then explain whether the Law of Sines or the Law of Cosines should be used to solve for p."