Transcript No Slide Title

If none of the angles of a triangle is a right
angle, the triangle is called oblique.
To solve an oblique triangle means to
find the lengths of its sides and the
measurements of its angles.
A
S
A
ASA
S
A
A
SAA
CASE 1: ASA or SAA
S
A
S
CASE 2: SSA
S
A
S
CASE 3: SAS
S
S
S
CASE 4: SSS
Name the case
5
47o
7
(1)SSS
(2)SAS
(3)SSA
(4)ASA
Theorem Law of Sines
For a triangle with sides a , b, c and opposite
angles  ,  ,  , respectively,
sin  sin  sin 


a
b
c
Proof (one case)
a
b
h

opp h
sin  
 , so h  b sin 
hyp b

opp h
sin  
 , so h  a sin 
hyp a
h  b sin   a sin 
sin 
sin 

a
b
Solve the triangle:  = 30 ,   70 , a  5 (SAA)


      180


30
b
30  70    180



  80

c




sin
30
sin
70
sin
30
sin
80

 70


5
b
5
c
5


5 sin 70
5 sin 80
b

9
.
40
c


9
.
85


sin 30
sin 30
Solve the triangle: c  5, b  3,   50 (SSA)

sin 50 sin 

3
5

5 sin 50
sin  
3

3
5

50
a
sin   128
.
No triangle with the given
measurements!
Which numbers not allowed in LOS
problem for sin α?
(1) -0.7 (2) 0 (3) 0.7 (4) 1.4