Question

What are the three situations when you can use the Law of Sines.

1 You are given a triangle with two angles and the included side.
2 You are given a triangle with all three sides.
3 You are given a triangle with two sides and a non-included angle.
4 You are given a triangle all three angles.
5 You are given a triangle with two angles and a non-included side.

Answer 1

The Sine Law has the following equations

sinA/a = sinB/b = sinC/c

From these equations, in order to use the ratios, you must know at least one angle and two sides, or at least one side and 2 angles. It doesn't matter if it's included or not, as long as you are given the angles. Because you could related the three equations with each other.

The answer is 1, 3 and 5.

Answer 2

Answer with explanation:

Law of Sines

If the triangle has side length, a , b and c and Angles are A, B and C , then Sine law can be written as

`(a)/(\sin A)=(b)/(\sin B)=(c)/(\sin C)`

1. You are given a triangle with two angles and the included side.

Find the measure of third Angle, then using sine law find the length of other sides.

3.You are given a triangle with two sides and a non-included angle.

First evaluate , second angle which is in front of corresponding side and then third angle and other side.

5.You are given a triangle with two angles and a non-included side.

Calculate the third Angle using angle sum property and other sides using sine law.