Section 6.1.3 Day 2
The Ambiguous Case of the
Law of Sines

Lesson Objective:
Students will:
• Solve triangles that could have more than one solution.
• Extend their understanding of the inverse sine and cosine functions to triangles.

Group Objective:
Students will:
• Do problems 6-35 to 6-37.
• Copy Math Notes into spiral.

Law of Sines Steps
When one angle and two sides side are given:
1) Solve for one angle.
2) Find the supplement of the angle found in step 1.
3)Two triangles are formed.
a)One triangle formed with the angle found with LOS in Step 1.
b)Second triangle formed with the supplement found in step 2.
c)Draw both triangles.
d)Find the other parts of each triangle.

Closure
Solve ABC if A=60°, b=50 and a=45.
50
A
60°
C
45
B
2 Triangles

Closure (cont.)
50
A
60°
C
45
B
C = 45.8, c = 37.3

Closure (cont.)
C
50 45
A
60°
B
C = 14.2, c = 12.7

Pg 270 #6-10 TO 6-18

Example 1
Solve ABC if A=60°, b=50 and a=33.
50
A
60°
C
33
No Triangle, no solution
B

Example 2
Solve ABC if A=60° b=50 and a=65
C
50
A
60°
65
1 Triangle
B

Example 2 (cont.)
B = 41.8, C = 78.2, c = 73.5