The Ambiguous Case (Ssa) Cheat Sheet
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4DO NOW
WS
Draw a picture of triangle RST and solve
1) C = 50°, b = 21.1, c = 16.4
for missing sides and angles.
2) A = 4.45°, b = 142.4, c = 135.5
3) A = 79.2°, a = 7.1, c = 5.6
R
R = 30°
30°
r = _____
4) B = 69.59°, b = 20, a = 18
S = 40°
s = 5.92
5) C = 71.2°, b = 24.5, a = 18.7
T = _____
t = _____
6) A = 69°, b = 12.02, c = 8.37
7) 26 ft
The Ambiguous Case (SSA)
To solve a triangle using the Law of Sines,
Continuing Section 9.3 –
given SSA, the situation is ambiguous.
(SSA
2 sides and a non‐included angle)
Law of Sines
Th
The given measures may form 0, 1, or 2
i
f
0 1
2
triangles.
Ambiguous Case
We go through a series of tests to determine
how many solutions exist.
The Ambiguous Case (SSA)
The Ambiguous Case (SSA)
Situation I: Angle A is OBTUSE
In our examples, the given angle will always
be A, and the given sides will always be
If angle A is obtuse there are TWO possibilities:
a and b.
If
If a > b, then there is
b th
th
i
If a ≤ b, then a is too
We don’t know what
one triangle with
short to reach side c.
these dimensions.
angle C is, so we can’t
C = ?
NO SOLUTION
draw side a in the right
ONE SOLUTION
C = ?
C = ?
a
position.
b
a
a
b
b
A
B = ?
c = ?
A
B ?
A
B ?
c = ?
c = ?
1
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