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Algebra 2: Unit 10: Law of Sines
NAME: _____________________________
Solve the right triangles by finding all the missing parts.
1.
A
2.
X
12
c
b
6
36
B
C
Y
z
9
B=
A=
X=
b=
c=
z=
Y=
Now we are going to solve triangles that have no right angles, using similar techniques.
C
Use when you have….
a
b
A
B
c
Law of Sines…
Examples: Find the remaining sides and angles.
C
1.
a
27 102
28
B
c
A
E
2.
f
d
D
96
23
30
F
.
The Ambiguous Case (SSA)
If the given angle < 90 , then test for 4 possible cases.
Case 1: No Solution
Case 2: One Solution
Ex: a = 15, b = 25, and A = 85
Ex: a = 4, b = 8, and A = 30
Case 3: Two Solutions
Case 4: One Solution
Ex: a = 12, b = 31, and A = 20.5
Ex: a = 22, b = 12, and A = 42
Case 1: No Solution
Ex: a = 25, b =30 , and A = 117
If the given angle > 90 , then test for 2 possible cases.
Case 2: One Solution
Ex: a = 28, b = 24, and A = 125
Practice: Use the Law of Sines to solve for the missing sides and angles of the triangle (if possible).
1. B = 150 , b = 30, c = 10
2. B = 150 , a = 10, b = 3
3. A = 75 , a = 51.2, b = 33.7
4. B = 25 , a = 6.2, b = 4