1. Section 7.1
The Law of Sines

2. A
B
C a
c
b

3. c
C
b
B
a
A sinsinsin

Answers on next slide.

4. sin40
4
=
sin60
b
b =
sin60
sin40
*4 » 5.39
sin40
4
=
sin80
c
c =
sin80
sin40
*4 » 6.13

5. c
C
b
B
a
A sinsinsin

Solve the triangle:
4,80,45  bCB
45
80
A
a
c
4
Answers on next slide.

6. Section 7.3
The Law of Cosines

7. ab
cba
C
ac
bca
B
bc
acb
A
2
cos
2
cos
2
cos
222
222
222





 A
B
C a
c
b

8. 8© 2011 Pearson Education, Inc. All rights reserved
EXAMPLE 1 Solving SAS Triangles
Solve triangle ABC with a = 15 inches,
b = 10 inches, and C = 60º. Round each answer
to the nearest tenth.Solution
Step 1 Find side c opposite the given angle C.
      
  
2 2 2
2 22
2
15 110 1
2 cos
2 c 6os
1
225 100 2 15 10 175
2
175
0
1
0°
.2
5
3
c
c
c
ba ab C
c
  
  
 
    
 
 

9. 9© 2011 Pearson Education, Inc. All rights reserved
Solution continued
1
sin sin
sin
sin
10sin60°
sin
175
10sin60°
sin 40.9°
175
B C
b c
b C
B
c
B
B 



 
  
 
EXAMPLE 1 Solving the SAS Triangles
Step 2 Find the angle B opposite side b.

10. 10© 2011 Pearson Education, Inc. All rights reserved
Solution continued
EXAMPLE 1 Solving the SAS Triangles
Step 3 Use the angle sum formula to find the
third angle.
Step 4 The solution of triangle ABC is
180° 60° 40.9° 79.1°A    
A ≈ 79.1° a = 15 inches
B ≈ 40.9° b = 10 inches
C = 60° c ≈ 13.2 inches

11. Set these up:
1. B = 20o a = 10 c = 15
2. A = 25o b = 3 c = 6
3. C = 75o a = 5 b = 3
4. B = 45o a = 8 c = 82
5. A = 60o b = 3 c = 6
6. C = 30o a = 24 b = 123
Set these up
and solve:

12. 12© 2011 Pearson Education, Inc. All rights reserved
EXAMPLE 3 Solving the SSS Triangles
Solve triangle ABC with a = 3.1 feet,
b = 5.4 feet, and c = 7.2 feet. Round answers to
the nearest tenth.Solution
Step 1 Because c is the longest side, find C.
2 2 2
2 2 2
2 cos
2 cos
c a b ab C
ab C a b c
  
  
     
  
2 2 22 2 2
5
cos
7.4
0.39
2
3.1
3.12 5.4
.2cb
ab
a
C
  
   
 1
cos 0.39 113°C 
  

13. 13© 2011 Pearson Education, Inc. All rights reserved
Solution continued
sin sinB C
b c

EXAMPLE 3 Solving the SSS Triangles
Step 2 Find B.
1
1
sin
sin
sin
sin
5.4sin113°
sin 43.7°
7.2
b C
B
c
b C
B
c



 
  
 
 
  
 

14. 14© 2011 Pearson Education, Inc. All rights reserved
Solution continued
Step 3 A ≈ 180º − 43.7º − 113º ≈ 23.3º
Step 4 Write the solution.
EXAMPLE 3 Solving the SSS Triangles
A ≈
23.3°
a = 3.1 feet
B ≈
43.7°
b = 5.4 feet
C ≈
113°
c = 7.2 feet

15. Example
a=5, b=7, c=8, find cosine of greatest angle.
15© 2011 Pearson Education, Inc. All rights reserved