Transcript No Slide Title

To solve an oblique triangle means to
find the lengths of its sides and the
measurements of its angles.
Theorem Law of Sines
For a triangle with sides a , b, c and opposite
angles  ,  ,  , respectively,
sin  sin  sin 


a
b
c
We use the Law of Sines to solve CASE 1
(SAA or ASA) and CASE 2 (SSA) of an
oblique triangle. The Law of Cosines is
used to solve CASES 3 and 4.
CASE 3: Two sides and the included
angle are known (SAS).
CASE 4: Three sides are known (SSS).
Theorem Law of Cosines
For a triangle with sides a , b, c and opposite
angles  ,  ,  , respectively.
c  a  b  2ab cos
2
2
2
b  a  c  2ac cos 
2
2
2
a  b  c  2bc cos
2
2
2
Solve the triangle: b  3, c  4,  40 (SAS)

3

a


40
4
a  b  c  2bc cos
2
2
2
a  3  4  234 cos 40
2
a  6.614933365
2
2
2
a  2.57


3
2.57
2
2
2
 b  a  c  2ac cos 

40
4
2
2
2
a c b
cos  
2ac
6.6149  4  3

 0.6622
2(2.57)(4)
2
2
  48.5

  180  40  48.5



  915
.

Solve the triangle: a  3,b  5, c  7 (SSS)

3
5

7
2
2
2
a  b  c  2bc cos

5 7 3
cos 
2(5)(7)
2
2
2
b c a
65 13
cos 
cos  
2bc
70 14

  218
.
2
2
2

5
3

a c b
cos  
2ac
2
2

218
.
2
7
2
2
2
3 7 5
33 11



2(3)(7)
42 14
  38.2
  180  21.8  38.2  120