Algebra 2 CH 9.5 Apply the Law of Sines.notebook
Algebra 2 CH 9.5 Apply the Law of Sines.notebook
Apply the Law of Sines
Apply the Law of Sines How can we find unknown side lengths and angles when we do not have a right triangle?
9.5 Apply the Law of Sines •
August 30, 2013
Solving for unknown sides and angles using the Law of Sines
We will use the LAW OF SINES!
Apply the Law of Sines
Apply the Law of Sines
The triangle no longer has a hypotenuse, opposite and adjacent sides.
A
b
c
B
Law of Sines
C
a
Apply the Law of Sines
Apply the Law of Sines
A=115o b=11
c B
C
Pull
a=20
1
Algebra 2 CH 9.5 Apply the Law of Sines.notebook
Apply the Law of Sines
August 30, 2013
Apply the Law of Sines
A=107o b
c=15
C=25o
B
Pull
a
Apply the Law of Sines A c=?
Apply the Law of Sines A=85o
b c=?
Pull
C=51o
Apply the Law of Sines
a=11
B=44o
C=51o
Pull
a=11
B=44o
b
Apply the Law of Sines
Supplements Theorem
2
Algebra 2 CH 9.5 Apply the Law of Sines.notebook
Apply the Law of Sines
August 30, 2013
Apply the Law of Sines
If:
Find another angle that has the same sine value.
Apply the Law of Sines
Apply the Law of Sines c=16
A b=13
B=40o
C
Pull
a
Apply the Law of Sines
Apply the Law of Sines A=87.7o
c=16
b=13
B=40o
a
C=52.3o
3
Algebra 2 CH 9.5 Apply the Law of Sines.notebook
Apply the Law of Sines
August 30, 2013
Apply the Law of Sines
A=?
A=?
c=16
c=16 b=13
a
B=40o
C=127.7o
b=13
a
B=40o
C=127.7o
Supplements Theorem
Apply the Law of Sines
Apply the Law of Sines
A b=11
c=9
a
C
Pull
B=75o
Apply the Law of Sines A=115o b=11
c B
a=20
C
Pull
Apply the Law of Sines
4
Algebra 2 CH 9.5 Apply the Law of Sines.notebook
Apply the Law of Sines
August 30, 2013
Apply the Law of Sines A=115o b=11
c B
Apply the Law of Sines
Apply the Law of Sines A
A=115o B
B
C
a=20
b
c
b=11
c
C
a=20
a
C
Using trigonometry to find the area of a triangle.
Apply the Law of Sines
Apply the Law of Sines
A=115o b=11
c=14 B
a
C
5
Algebra 2 CH 9.5 Apply the Law of Sines.notebook
August 30, 2013
Apply the Law of Sines
Apply the Law of Sines
D
When has the Law of Sines been used for a practical purpose? You can use the Law of Sines to find out how high a mountain is without having to climb the mountain.
A
25o 150m
38o B
C
Apply the Law of Sines
Apply the Law of Sines D
13o a
A
25o 142o 38o 150m B
C
Apply the Law of Sines D
Apply the Law of Sines
13o
h
281.81m
A
25o 150m
38o B
C
6
Algebra 2 CH 9.5 Apply the Law of Sines.notebook
August 30, 2013
Apply the Law of Sines
Apply the Law of Sines
D 13o
9.5 Apply the Law of Sines
h =173.3
281.81m
A
25o 150m
•
Solving for unknown sides and angles using the Law of Sines
38o B
C
7
Apply the Law of Sines
Apply the Law of Sines How can we find unknown side lengths and angles when we do not have a right triangle?
9.5 Apply the Law of Sines •
August 30, 2013
Solving for unknown sides and angles using the Law of Sines
We will use the LAW OF SINES!
Apply the Law of Sines
Apply the Law of Sines
The triangle no longer has a hypotenuse, opposite and adjacent sides.
A
b
c
B
Law of Sines
C
a
Apply the Law of Sines
Apply the Law of Sines
A=115o b=11
c B
C
Pull
a=20
1
Algebra 2 CH 9.5 Apply the Law of Sines.notebook
Apply the Law of Sines
August 30, 2013
Apply the Law of Sines
A=107o b
c=15
C=25o
B
Pull
a
Apply the Law of Sines A c=?
Apply the Law of Sines A=85o
b c=?
Pull
C=51o
Apply the Law of Sines
a=11
B=44o
C=51o
Pull
a=11
B=44o
b
Apply the Law of Sines
Supplements Theorem
2
Algebra 2 CH 9.5 Apply the Law of Sines.notebook
Apply the Law of Sines
August 30, 2013
Apply the Law of Sines
If:
Find another angle that has the same sine value.
Apply the Law of Sines
Apply the Law of Sines c=16
A b=13
B=40o
C
Pull
a
Apply the Law of Sines
Apply the Law of Sines A=87.7o
c=16
b=13
B=40o
a
C=52.3o
3
Algebra 2 CH 9.5 Apply the Law of Sines.notebook
Apply the Law of Sines
August 30, 2013
Apply the Law of Sines
A=?
A=?
c=16
c=16 b=13
a
B=40o
C=127.7o
b=13
a
B=40o
C=127.7o
Supplements Theorem
Apply the Law of Sines
Apply the Law of Sines
A b=11
c=9
a
C
Pull
B=75o
Apply the Law of Sines A=115o b=11
c B
a=20
C
Pull
Apply the Law of Sines
4
Algebra 2 CH 9.5 Apply the Law of Sines.notebook
Apply the Law of Sines
August 30, 2013
Apply the Law of Sines A=115o b=11
c B
Apply the Law of Sines
Apply the Law of Sines A
A=115o B
B
C
a=20
b
c
b=11
c
C
a=20
a
C
Using trigonometry to find the area of a triangle.
Apply the Law of Sines
Apply the Law of Sines
A=115o b=11
c=14 B
a
C
5
Algebra 2 CH 9.5 Apply the Law of Sines.notebook
August 30, 2013
Apply the Law of Sines
Apply the Law of Sines
D
When has the Law of Sines been used for a practical purpose? You can use the Law of Sines to find out how high a mountain is without having to climb the mountain.
A
25o 150m
38o B
C
Apply the Law of Sines
Apply the Law of Sines D
13o a
A
25o 142o 38o 150m B
C
Apply the Law of Sines D
Apply the Law of Sines
13o
h
281.81m
A
25o 150m
38o B
C
6
Algebra 2 CH 9.5 Apply the Law of Sines.notebook
August 30, 2013
Apply the Law of Sines
Apply the Law of Sines
D 13o
9.5 Apply the Law of Sines
h =173.3
281.81m
A
25o 150m
•
Solving for unknown sides and angles using the Law of Sines
38o B
C
7
