5.9 Law of Sines

1. Law of Sines

1. 1. A way to find the sides and angles of a triangle when that triangle is NOT a right triangle.

2. 2. Used to find side and angle measures when given:

   • Two angle values and a side length

   • Two side lengths and an angle value (when the angle is NOT between the two sides)

1. Law of Sines

3. Examples: Find all sides and angles.

​1.

​2.

1. Label all angles A,B, and C.

2. Label the opposite sides a, b, and c.

3. Pick two angle-side pairs to write an equation using the law of sines.

4. Solve for the missing side/angle.

5. Use law of sines or Triangle Angle Sum

2. Things to know about missing angles with Law of Sines.

Caution:

---> It is possible to have one, two, or no solutions when finding angles.

Remember:

---> The sine function values are always between -1 and 1.

---> Positive sine values are in Quadrant I and II.

---> If given two angles, use Triangle Angle Sum Theorem:

180-angle-angle=missing angle.

---> NO triangle can have two angles bigger than 90°.

2. Examples: Find all sides and angles.

3.

​4.

1. Label all angles A,B, and C.

2. Label the opposite sides a, b, and c.

3. Pick two angle-side pairs to write an equation using the law of sines.

4. Solve for the missing side/angle.

5. Use law of sines or Triangle Angle Sum