2. Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Lesson 9.5 Apply the Law of Sines Warm-Up Standard Accessed: Students will prove, apply, and model trigonometric functions and ratios.

3. Warm-Up Solve Δ XYZ.

4. Solve Δ ABC.

5. Vocabulary Can be used to solve triangles with no right angle, when two angles and the length of any side are known (AAS or ASA cases), or when the lengths of two sides and an angle opposite one of the two sides are known, (SSA).

6. Essential Understandings When can the Law of sines be used to solve a triangle?  When two angles and the length of any side are known (AAS or ASA cases), or when the lengths of two sides and an angle opposite one of the two sides are known, (SSA). The law of sines is used to solve triangles with no right angle.

7. Solve a triangle for the AAS or ASA case EXAMPLE 1 SOLUTION 3. Write the Law of Sine proportion 1. Draw a picture 4. Write the Law of Sine proportion

8. Solve a triangle for the AAS or ASA case EXAMPLE 1 When you are given the measures of two angles and one side of a triangle, why does it not matter whether the given side is the one included between the two angles? It does not matter since you are given the measures of any two angles, you can always find the third angle measure. Key Question

9. Essential Understandings What are the possible triangles for the SSA case?

10. Solve the SSA case with one solution EXAMPLE 2 SOLUTION 3. Write the Law of Sine proportion 2. Draw a picture 5. Write the Law of Sine proportion

11. Examine the SSA case with no solution EXAMPLE 3 SOLUTION 2. Draw a picture What will happen if you try to solve the triangle by applying the law of sines and using your calculator? Write the Law of Sine proportion

12. Solve the SSA case with two solutions EXAMPLE 4 SOLUTION 3. Write the Law of Sine proportion 2. Draw a picture 5. Write the Law of Sine proportion

13. Vocabulary

14. Write and Solve a real – Use trig to find area of triangle EXAMPLE 4 KIS Vegetable Garden Esther and Frederick are setting up a triangular vegetable garden at KIS. They lay off lengths of 15ft and 11ft for two sides of the garden with a 62° angle between these two sides, what will be the area of the garden? 1. Draw a picture SOLUTION

15. Lesson 9.5 Homework: Practice B Practice C “Honors”