This document discusses using the Law of Sines to solve ambiguous triangle cases given two sides and a non-included angle (SSA). There can be 1, 2, or 0 solutions depending on whether the opposite side is greater than or less than the adjacent side. Examples are provided to practice solving SSA cases using the Law of Sines. Students are assigned a worksheet to practice solving ambiguous triangle cases.

1. PC_6.1B_Notes February 03, 2012
6.1 Continued…
Law of Sines
Objective: Use the law of sines to solve
the ambiguous case of a triangle
Standard: Trigonometry 13.0, 14.0
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2. PC_6.1B_Notes February 03, 2012
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 NON­included angle.
Three Possible Outcomes:
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3. PC_6.1B_Notes February 03, 2012
Here's how 2 triangles
are formed.
0°
234
12 19
52°
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4. PC_6.1B_Notes February 03, 2012
The Test for SSA ­
How you determine the number of solutions:
If opp ≥ adj, then __________
If opp < adj, then __________
The second solution: Then find B ,
1
A1 is the _______ angle found. C , and c
1 1
Second solution angle A2= _______
Then find B2, C2, and c2
You will have to complete the problem twice!
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5. PC_6.1B_Notes February 03, 2012
Ex. 1﴿ Use the Law of Sines to find the missing
sides and angles. Solutions?
A=48°, a=11.4, c=12.8
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6. PC_6.1B_Notes February 03, 2012
Ex. 2﴿ Use the Law of Sines to find the missing
sides and angles. Solutions?
A=76°, a=18, c=20
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7. PC_6.1B_Notes February 03, 2012
Ex. 3)
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8. PC_6.1B_Notes February 03, 2012
Ex. 4)
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9. PC_6.1B_Notes February 03, 2012
How do you know?
0 solutions:
1 solution:
2 solutions:
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10. PC_6.1B_Notes February 03, 2012
Assignment:
LOS: The
Ambiguous Case
WS
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11. PC_6.1B_Notes February 03, 2012
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12. PC_6.1B_Notes February 03, 2012
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13. PC_6.1B_Notes February 03, 2012
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