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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.

Verified Answer :

MissPhiladelphia

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 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

    \(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\)

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.