1. 9.1 Law of Sines

2. Law of Sines
Used to solve oblique s
( s that are NOT right s) OR

3. Case 1: 2 Angles & 1 side known(AAS or ASA)
Case 1: 2 Angles & 1 side known(AAS or ASA) Ex 1) Solve the triangle where A = 37 , B = 82 , and a = 23 B
C = 180 - 37 - 82
= 61
82 c a
= 23 A
37 C b

4. Case 1: 2 Angles & 1 side known Ex 1) Solve the triangle where
Case 1: 2 Angles & 1 side known Ex 1) Solve the triangle where A = 37 , B = 82 , and a = 23 B
82 c a
= 23 A
37 C b
a = 23 A = 37
b = 38 B = 82
c = 33 C = 61
answer when “solving” a

5. Case 2: 2 sides & 1 angle opposite one of those sides known
(Ambiguous) (ASS – can’t do but know case 2)
Case 2: 2 sides & 1 angle opposite one of those sides known
A known angle is obtuse
if a  b, then no
if a > b, then unique
A known angle is acute
sinB > 1 → no
sinB = 1 → right
0 < sinB < 1 → either or s
or 0 < sinB < 1

6. Ex 2) Solve the triangle where A = 123 , a = 14, b = 21
Obtuse
Impossible!!!
→ No
(Ambiguous Case with no solution)

7. Ex 3) Solve the triangle where A = 48 , a = 61, b = 32
Acute
Ex 3) Solve the triangle where A = 48 , a = 61, b = 32
Sine is (+)  B in QI or QII
B = sin-1(0.3898)
= 23°
Or B = 180° - 23° = 157°
But if B = 157° and A = 48°
Not possible since > 180
So, B = 23°
C = 180° - 48° - 23° = 109°

8. Ex 3) Solve the triangle where A = 48 , a = 61, b = 32
b = B = 23°
c = C = 109°
(Ambiguous Case
w/ unique solution)

9. Homework
#901 Pg – 12 all