Algebra 2 CH 9.6 Apply the Law of Cosines.notebook
Algebra 2 CH 9.6 Apply the Law of Cosines.notebook
Apply the Law of Cosines
9.6 Apply the Law of Cosines • Solving for unknown sides and angles using the Law of Cosines
Apply the Law of Cosines
a
Apply the Law of Cosines
C
Apply the Law of Cosines A
b=14
c a=11
Apply the Law of Cosines
SAS C=34o
Pull
B
Not every case allows the application of the Law of Sines, so when you do not have enough information for the Law of Sines, use the Law of Cosines.
b
c B
Apply the Law of Cosines
Law of Cosines
We are still going to use the same type of triangle as we used with the Law of Sines.
A
August 30, 2013
1
Algebra 2 CH 9.6 Apply the Law of Cosines.notebook
Apply the Law of Cosines A=20o
c=5.2 B
b=5
August 30, 2013
Apply the Law of Cosines
SAS C
Pull
a
Apply the Law of Cosines The distance between the earth and the star Sirius is 8.4 light years. The distance between the star Alpha Centauri and Earth is 4.3 light years. The angle formed by the two stars and Earth, with Earth being the vertex is 44o. What is the distance between the stars?
Apply the Law of Cosines
? 8.4
44o 4.3
First draw a picture!
Apply the Law of Cosines C
Apply the Law of Cosines
b A
a=8.4
c=4.3
Pull
B=44o
2
Algebra 2 CH 9.6 Apply the Law of Cosines.notebook
Apply the Law of Cosines
August 30, 2013
Apply the Law of Cosines C
C
b=20 A
a=27
c=12
In this situation, we know the lengths of all 3 sides, but we do not know the measurement of any angles.
Find the measurement of angle C.
B
SSS
b=20 A
c=12
a=27
B
Apply the Law of Cosines
Apply the Law of Cosines
Apply the Law of Cosines
Apply the Law of Cosines
C=24.2 o
b=20 A
c=12
a=27
B
3
Algebra 2 CH 9.6 Apply the Law of Cosines.notebook
Apply the Law of Cosines
August 30, 2013
Apply the Law of Cosines A golfer hits a ball 260 yards on a hole that is 400 yards long. The shot is 15o off target. What is the distance from the golfer's ball to the hole? 260 yds
15
c
o
400 yds
Apply the Law of Cosines
Apply the Law of Cosines
260 yds
c=163.4
15o
400 yds
Apply the Law of Cosines
Apply the Law of Cosines
What is the maximum angle at which the golfer can be off target in order to land no more than 10 yards from the hole? Co
10 yds
163.4 yards
First we must find the hypotenuse!
4
Algebra 2 CH 9.6 Apply the Law of Cosines.notebook
Apply the Law of Cosines
August 30, 2013
Apply the Law of Cosines
163.7 yards Co
10 yds
163.4 yards
Apply the Law of Cosines
Apply the Law of Cosines
Apply the Law of Cosines
Apply the Law of Cosines
Co
163.4 yards
10 yds
Which law would you use: Sines or Cosines?
24 50o
21
Pull
163.7 yards
COSINES
x
5
Algebra 2 CH 9.6 Apply the Law of Cosines.notebook
August 30, 2013
Which law would you use: Sines or Cosines?
Which law would you use: Sines or Cosines?
35
9 xo
SINES
25o
Apply the Law of Cosines Heron's Area Formula
Pull
Apply the Law of Cosines
Pull
Apply the Law of Cosines
19
17
COSINES
4
Apply the Law of Cosines Find the area of the triangle:
The area of any triangle can be found with the formula:
7
4
9 where
Apply the Law of Cosines
Apply the Law of Cosines
6
Algebra 2 CH 9.6 Apply the Law of Cosines.notebook
August 30, 2013
Apply the Law of Cosines
9.6 Apply the Law of Cosines • Solving for unknown sides and angles using the Law of Cosines
7
Apply the Law of Cosines
9.6 Apply the Law of Cosines • Solving for unknown sides and angles using the Law of Cosines
Apply the Law of Cosines
a
Apply the Law of Cosines
C
Apply the Law of Cosines A
b=14
c a=11
Apply the Law of Cosines
SAS C=34o
Pull
B
Not every case allows the application of the Law of Sines, so when you do not have enough information for the Law of Sines, use the Law of Cosines.
b
c B
Apply the Law of Cosines
Law of Cosines
We are still going to use the same type of triangle as we used with the Law of Sines.
A
August 30, 2013
1
Algebra 2 CH 9.6 Apply the Law of Cosines.notebook
Apply the Law of Cosines A=20o
c=5.2 B
b=5
August 30, 2013
Apply the Law of Cosines
SAS C
Pull
a
Apply the Law of Cosines The distance between the earth and the star Sirius is 8.4 light years. The distance between the star Alpha Centauri and Earth is 4.3 light years. The angle formed by the two stars and Earth, with Earth being the vertex is 44o. What is the distance between the stars?
Apply the Law of Cosines
? 8.4
44o 4.3
First draw a picture!
Apply the Law of Cosines C
Apply the Law of Cosines
b A
a=8.4
c=4.3
Pull
B=44o
2
Algebra 2 CH 9.6 Apply the Law of Cosines.notebook
Apply the Law of Cosines
August 30, 2013
Apply the Law of Cosines C
C
b=20 A
a=27
c=12
In this situation, we know the lengths of all 3 sides, but we do not know the measurement of any angles.
Find the measurement of angle C.
B
SSS
b=20 A
c=12
a=27
B
Apply the Law of Cosines
Apply the Law of Cosines
Apply the Law of Cosines
Apply the Law of Cosines
C=24.2 o
b=20 A
c=12
a=27
B
3
Algebra 2 CH 9.6 Apply the Law of Cosines.notebook
Apply the Law of Cosines
August 30, 2013
Apply the Law of Cosines A golfer hits a ball 260 yards on a hole that is 400 yards long. The shot is 15o off target. What is the distance from the golfer's ball to the hole? 260 yds
15
c
o
400 yds
Apply the Law of Cosines
Apply the Law of Cosines
260 yds
c=163.4
15o
400 yds
Apply the Law of Cosines
Apply the Law of Cosines
What is the maximum angle at which the golfer can be off target in order to land no more than 10 yards from the hole? Co
10 yds
163.4 yards
First we must find the hypotenuse!
4
Algebra 2 CH 9.6 Apply the Law of Cosines.notebook
Apply the Law of Cosines
August 30, 2013
Apply the Law of Cosines
163.7 yards Co
10 yds
163.4 yards
Apply the Law of Cosines
Apply the Law of Cosines
Apply the Law of Cosines
Apply the Law of Cosines
Co
163.4 yards
10 yds
Which law would you use: Sines or Cosines?
24 50o
21
Pull
163.7 yards
COSINES
x
5
Algebra 2 CH 9.6 Apply the Law of Cosines.notebook
August 30, 2013
Which law would you use: Sines or Cosines?
Which law would you use: Sines or Cosines?
35
9 xo
SINES
25o
Apply the Law of Cosines Heron's Area Formula
Pull
Apply the Law of Cosines
Pull
Apply the Law of Cosines
19
17
COSINES
4
Apply the Law of Cosines Find the area of the triangle:
The area of any triangle can be found with the formula:
7
4
9 where
Apply the Law of Cosines
Apply the Law of Cosines
6
Algebra 2 CH 9.6 Apply the Law of Cosines.notebook
August 30, 2013
Apply the Law of Cosines
9.6 Apply the Law of Cosines • Solving for unknown sides and angles using the Law of Cosines
7
