1. 1) State the LAW OF SINES. 2) Find a. Students,
Take out your calendar and your homework. Take out your spiral notebook and Complete the DNA. Use your notes if necessary.
1) State the LAW OF SINES.
2) Find a.

2. Example: No-Solution Case - SSA
Example (SSA):
Use the Law of Sines to solve the triangle.
A = 76, a = 18 inches, b = 20 inches C A B
b = 20 in
a = 18 in
76
There is no angle whose sine is
There is no triangle satisfying the given conditions.
Example: No-Solution Case - SSA

3. Section 6.1, The Ambiguous Case (SSA) Table, pg. 394

4. Example: Two-Solution Case - SSA
Example (SSA):
a = 11.4 cm C A B1
b = 12.8 cm c
58
Use the Law of Sines to solve the triangle.
A = 58, a = 11.4 cm, b = 12.8 cm
49.8
72.2
10.3 cm
C  180 – 58 – 72.2 = 49.8
Two different triangles can be formed.
Example continues.
Example: Two-Solution Case - SSA

5. Example: Two-Solution Case – SSA continued
Example (SSA) continued:
72.2
10.3 cm
49.8
a = 11.4 cm C A B1
b = 12.8 cm c
58
Use the Law of Sines to solve the second triangle.
A = 58, a = 11.4 cm, b = 12.8 cm
B2  180 – 72.2 = 
C  180 – 58 – 107.8 = 14.2 C A B2
b = 12.8 cm c
a = 11.4 cm
58
14.2
107.8
3.3 cm
Example: Two-Solution Case – SSA continued

6. Area of an Oblique TriangleC B A b c a
Find the area of the triangle.
A = 74, b = 103 inches, c = 58 inches
Example:
103 in
74
58 in
Area of an Oblique Triangle

7. The flagpole is approximately 9.5 meters tall.
Application:
A flagpole at a right angle to the horizontal is located on a slope that makes an angle of 14 with the horizontal. The flagpole casts a 16-meter shadow up the slope when the angle of elevation from the tip of the shadow to the sun is 20.
20 A
70
Flagpole height: b
34 B
16 m C
14
The flagpole is approximately 9.5 meters tall.
Application

10. Complete each identity.