3.4 Ambiguous Case

3.4 Ambiguous Case
3.4 The Ambiquous Case
A cute ASS
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3.4 Ambiguous Case
Here's the rub....
We are given an angle, and two sides (ASS)
Side
Side
Side
Side
θ
θ
Angle
Angle
4 possibilities
2 possibilites
Depending on what information you are provided with regarding the
triangle you want to solve...there are two possibilities
1. If SSS, SAS, ASA, or AAS then
there is only one possibility
2. If ASS then there are many possibile outcomes
Acute angle given: 4 possibilities
Obtuse angle given: 2 possibilities
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3.4 Ambiguous Case
Case 1- the Acute angle
Side
Side
θ
Angle
If b < c Sin B then no triangle is possible
If b = c Sin B then one triangle is possible
If cSin B < b < c then two triangles are possible
If b > c then one triangle is possible
A
c
B
cSin B
C
Case 2- the Obtuse angle
If b > c Sin B then one triangle is possible
If b < c then no triangle is possible
b
c
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3.4 Ambiguous Case
Example
How many triangles can be drawn,if any, having angle P = 51o,
q = 12, and p =10? Solve each.
Example
Can one draw a ΔXYZ in which <Z = 125o, z = 8.44, and x = 6.53. If
so, how many triangles exist? Solve each.
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