Section 5.7: The Ambiguous Case of the Law of

```Section 5.7: The Ambiguous Case of the Law of Sines
September 16, 2014
5-7: Solving Triangles for Ambiguous
Cases of the Law of Sines
(SSA combination)
1.) Decide how many solutions there are
Remember, this only matters if you are given
SSA. Otherwise, just solve!
2.) Use the Law of Sines to find an angle first.
3.) Find the other angle and the last side.
Sep 23­8:44 AM
height - drawn from
the vertex between
the two given sides
1.) A = 36°, a = 2, c = 7
Sep 23­8:53 AM
Section 5.7: The Ambiguous Case of the Law of Sines
September 16, 2014
height - drawn from
the vertex between
the two given sides
2.) B = 106°, a = 17, b = 25
Sep 23­8:53 AM
Construction #3: Suppose ∠A is acute & side a is smaller than side c
Recall from yesterday the constructions in which two triangles
were formed from SSA
Sep 23­8:51 AM
Section 5.7: The Ambiguous Case of the Law of Sines
September 16, 2014
Construction #3: Suppose ∠A is acute & side a is smaller than side c
Recall from yesterday the constructions in which two triangles
were formed from SSA
Sep 23­8:51 AM
The only way to get two solutions
This is very rare! Only happens with 1 out of the 6 SSA combinations!
Angle-Side-Side
Given angle is acute
opposite side is smaller than adjacent, but bigger than the height.
c
a
Find angle "C" by the
Law of Sines then solve
that triangle
A
For the second triangle
take 180-"C", then solve
that triangle.
c
a
"C" = angle across from
A
Sep 24­7:27 AM
Section 5.7: The Ambiguous Case of the Law of Sines
September 16, 2014
The only way to get two solutions
This is very rare! Only happens with 1 out of the 6 SSA combinations!
Angle-Side-Side
Given angle is acute
opposite side is smaller than adjacent, but bigger than the height.
c
Find angle "C" by the
Law of Sines then solve
that triangle
a
A
For the second triangle
take 180-"C", then solve
that triangle.
c
a
"C" = angle across from
A
Sep 24­7:27 AM
height - drawn from
the vertex between
the two given sides
3.) B = 37°, a = 32, b = 27
Sep 23­8:53 AM
Section 5.7: The Ambiguous Case of the Law of Sines
September 16, 2014
height - drawn from
the vertex between
the two given sides
4.) C = 90°, a = 8, c = 7
Sep 23­8:53 AM
height - drawn from
the vertex between
the two given sides
5.) A = 58°, C = 94°, b = 17
Sep 23­8:53 AM
```