More work on the law of sines, including testing for the ambiguous case.

1. January 11, 2011
6.1 Continued…
Law of Sines
Objective: 1) Use the law of sines to
solve the ambiguous case of a triangle,
2) Find the area of a triangle.
Standard: Trigonometry 13.0, 14.0

2. January 11, 2011
The Ambiguous Case: SSA
SSA is not a congruency property from
Geometry, so we need to be careful
when solving a triangle given two sides
and the NON-included angle.
Three Possible Outcomes:
· 1 Triangle formed
· 2 Triangles formed
· 0 Triangles formed

3. January 11, 2011
Here's how 2 triangles
are formed.
0°
232
12 19
52°

4. January 11, 2011
The Test for SSA -
How you determine the number of solutions:
If opp ≥ adj, then __________
If opp < adj, then __________
The second solution: Then find B1,
A is the _______ angle found. C1, and c1
1
Second solution angle A2= _______
Then find B2, C2, and c2
You will have to complete the problem twice!

5. January 11, 2011
Ex. 1) Use the Law of Sines to find the missing
sides and angles. Solutions?
A=110°, a=125, b=100

6. January 11, 2011
Ex. 2) Use the Law of Sines to find the missing
sides and angles. Solutions?
A=76°, a=18, c=20

7. January 11, 2011
Ex. 3) Use the Law of Sines to find the missing
sides and angles. Solutions?
A=48°, a=11.4, c=12.8
Continues…

8. January 11, 2011
Ex. 3B) Use the Law of Sines to find the
missing sides and angles.
A=48°, a=11.4, c=12.8

9. January 11, 2011
Summary for solutions
to triangles…
0 solutions: you get an error!
1 solution: opp>adj and you get an answer.
2 solutions: opp<adj and you get an answer.
Oh, and you need to do the problem twice!

10. January 11, 2011
One more thing…
The area of a triangle:
With our new-found Law of Sines, we
can also use:

11. January 11, 2011
Ex. 4) Find the area of the triangle if
A=74°, b=103 ft. and c=58 ft.

12. January 11, 2011
Homework:
#2 Law of Sines WS
#11-30 (start at #21)