1. Lesson Objective
Analyze the ambiguous case of the sine law, and solve problems that involve the ambiguous case

2. “Ambiguous”
The word “Ambiguous” means something that can have more than one interpretation, More than one answer.

3. Consider the Following
Martina and Carl are both holding a rope that attached to a balloon in the sky.
Martina’s rope is 7.8 m long and makes a 36o angle with the ground
Carl’s rope is 5.8 m long
How far are Martina and Carl away from each other?

4. Consider the Following
there is an unfinished triangle.
With a ruler, draw a 5.8 cm line from point A to the ground. Then using a protractor, measure the angle.
Is there only one solution? In other words, is there only one triangle that can be made?

5. 7.8 M
5.8 m
5.8 m
36O

6. 7.8 M
5.8 m
5.8 m
36O
130o
50o

7. Triangle 1 Triangle 2 Sin 130o 7.8 m Sin 36o 5.8 m Sin 50o 7.8 m= =

8. BOTH TRIANGLES ARE POSSIBLE!
7.8 M
5.8 m
5.8 m
130o
50o
36o
Triangle 1
Triangle 2
0.766
7.8 m
Sin 36o
5.8 m
0.766
7.8 m
Sin 36o
5.8 m = =

9. Summary
In problems when you are given two sides and an angle (SSA), there can be more than one triangle formed.

10. There are Four SSA Scenarios
The side is not long enough
No triangle is possible
12 m
4 m
30o

11. There are Four SSA Scenarios
The side length is JUST “right”
One triangle is possible
12 m
6 m
30o

12. There are Four SSA Scenarios
The side length is longer than 6 m, but shorter than 12
Two triangles are possible
12 m
8 m
8 m
30o

13. There are Four SSA Scenarios
The side length is longer than 12 m
Only ONE triangle is possible
12 m
15 m
30o