1. Ambiguous Case AKA – Distinct Triangles

2. We use this method to determine how many triangles can be built with some given information. How do we know when to use this method? 1.It will ask one of the following: 1.How many triangles… 2.How many distinct triangles… 3.How many different triangles… The answer is always 0, 1, or 2. 0 is the least number that can be made and two is the most! Steps: 1.Use law of sines to find unknown 2.Build table and fill in missing angles 3.Determine number of triangles from table

3. 123 Angle 1 is always the angle given! 30 Angle 2 is always the angle you found and its supplement! 39 180-39=141 141 Angle 3 is determined by the first two angles in each row. Are there enough degrees left to form a triangle? 30+39=69 180-69=111 111 30+141=171 180-171=9 9 We were able to form 2 distinct triangles based on the chart! PAGE 7

4. 123 Angle 1 is always the angle given! 120 Angle 2 is always the angle you found and its supplement! 60 180-60=120 120 Angle 3 is determined by the first two angles in each row. Are there enough degrees left to form a triangle? 120+60=180 180-180=0 120+120=240 We were able to form 0 distinct triangles based on the chart! PAGE 7

5. 123 Angle 1 is always the angle given! 35 Angle 2 is always the angle you found and its supplement! 55 180-55=125 125 Angle 3 is determined by the first two angles in each row. Are there enough degrees left to form a triangle? 35+55=90 180-90=90 35+125=160 180-160=20 We were able to form 2 distinct triangles based on the chart! 90 20 PAGE 7

6. 123 Angle 1 is always the angle given! 48 Angle 2 is always the angle you found and its supplement! 73 180-39=141 107 Angle 3 is determined by the first two angles in each row. Are there enough degrees left to form a triangle? 48+73=121 180-121=59 59 48+107=155 180-155=25 25 We were able to form 2 distinct triangles based on the chart! PAGE 7

7. 123 Angle 1 is always the angle given! 45 Angle 2 is always the angle you found and its supplement! 40 180-40=140 140 Angle 3 is determined by the first two angles in each row. Are there enough degrees left to form a triangle? 45+40=85 180-85=95 95 45+140=185 We were able to form 2 distinct triangles based on the chart! PAGE 7

8. We were able to form 0 distinct triangles. PAGE 8

9. PAGE 6

10. Homework Page 8 #1-5,7