5.9 Law of Sines

Unit 5: Trigonometry

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)

Multiple Select

On which triangles can we use the law of sines?

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

Multiple Choice

Calculate the length of AC

• 30

• 24

• 27

• 35

Multiple Choice

Calculate the length of BC

• 24

• 20

• 27

• 23

Multiple Choice

Find AB

• 10

• 8

• 6.1

• 4.9

Multiple Choice

Find AC

• 12

• 10

• 23

• 14

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

Multiple Choice

What is the measure of angle A?

• 50 degrees

• 60 degrees

• 78 degrees

• 74 degrees

Multiple Choice

Find m<B

• A

• B

• C

• D

Multiple Choice

Calculate the length of BC

• 24

• 20

• 27

• 23

Multiple Choice

What is the measure of angle A?

• 58 degrees

• 61 degrees

• 78 degrees

• 74 degrees