Question

If ∠P and ∠R are given, as well as the value of p, then explain whether the Law of Sines or the Law of Cosines should be used to solve for r.

Law of Cosines, two sides and the included angle are known

Law of Cosines, all sides are known

Law of Sines, two angles and an opposite side are known

Law of Sines, two sides and an opposite angle are known

Answer 1

Law of Sines, two angles and an opposite side are known

Explanation:

We know that...

In order to use the Law of Sines:

• 2 sides and an opposite angle must be given to find another angle
• 2 angle and an opposite side must be given to find another side

In order to use the Law of Cosines:

• 2 sides and the angle between them must be given to find the third side
• all 3 sides must be given to find the angle

So now we know that there are 2 angles and an opposite side given. So that leads us to the answer: Law of Sines, two angles and an opposite side are known.

Answer 2

Law of Sines

Explanation:

You know two angles (∠P and ∠R) and the opposite side of ∠P (p).