Download Example 2 Find all missing sides and angles.

Algebra 3
Section 9.3 Lesson
Section 9.3
Law of Sines
Area of a triangle
K = / ab sinC = / bc sinA = / ac sinB
1
2
Law of Sines
1
2
sinC = sinA = sinB
c
a
b
Example 1
Find all missing sides and angles.
82ο
70ο
12
Example 2
Find all missing sides and angles.
10
30ο
110 ο
1
2
When do you use Law
of Sines?
ASA / AAS / SSA
Algebra 3
Section 9.3 Lesson
Construct the following three triangles.
1)
A = 30 ο b = 10 a = 4
2)
A = 30 ο b = 10 a = 5
3)
A = 30 ο b = 10 a = 6
b
m
0c
1
=
3
Test for number of possible triangles
Note: the value on the left side of the inequality is opposite of the angle
1)
a < bsinA
then no triangle exist
2)
a = bsinA
then one triangle exist
3)
a > bsinA and a < b
then two triangles exist
4)
a > bsinA and a ≥ b
then one triangle exist
Example 3
ΔXYZ X = 30ο
x=3
y=8
Algebra 3
Section 9.3 Lesson
Example 4
How many triangles exist? If any triangle(s) exist find all sides and angles.
ΔRST
S = 40ο
r = 30
s = 20