algebra 2 ch 9.6 apply the law of cosines.notebook · apply the law of cosines apply the law of...
TRANSCRIPT
Algebra 2 CH 9.6 Apply the Law of Cosines.notebook
1
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
Apply the Law of Cosines
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.
Apply the Law of Cosines
A
B C
c
a
b
We are still going to use the same type of triangle as we used with the Law of Sines.
Apply the Law of CosinesLaw of Cosines
Apply the Law of Cosines
A
B C=34oc
a=11
b=14
Pull
Pull
SASApply the Law of Cosines
Algebra 2 CH 9.6 Apply the Law of Cosines.notebook
2
August 30, 2013
Apply the Law of CosinesA=20o
B C
c=5.2
a
b=5
Pull
Pull
SAS
Apply the Law of Cosines
Apply the Law of CosinesThe 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?
First draw a picture!
Apply the Law of Cosines
8.44.3
?
44o
Apply the Law of Cosines
Pull
Pull
B=44o
A
C
c=4.3
b
a=8.4
Apply the Law of Cosines
Algebra 2 CH 9.6 Apply the Law of Cosines.notebook
3
August 30, 2013
Apply the Law of Cosines
B
A
C
c=12
b=20
a=27
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.
Apply the Law of Cosines
B
A
C
c=12
b=20
a=27
SSS
Apply the Law of Cosines Apply the Law of Cosines
Apply the Law of Cosines
B
A
C=24.2o
c=12
b=20
a=27
Apply the Law of Cosines
Algebra 2 CH 9.6 Apply the Law of Cosines.notebook
4
August 30, 2013
Apply the Law of Cosines 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?
400 yds
260 yds
15oc
Apply the Law of Cosines Apply the Law of Cosines
400 yds
260 yds
15oc=163.4
Apply the Law of Cosines
10 ydsCo
163.4 yards
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?
First we must find the hypotenuse!
Apply the Law of Cosines
Algebra 2 CH 9.6 Apply the Law of Cosines.notebook
5
August 30, 2013
Apply the Law of Cosines
10 ydsCo
163.4 yards
163.7 yards
Apply the Law of Cosines
Apply the Law of Cosines Apply the Law of Cosines
Apply the Law of Cosines
10 ydsCo
163.4 yards
163.7 yards
Apply the Law of Cosines
Which law would you use: Sines or Cosines?
24 2150o
x
Pull
Pull
COSINES
Algebra 2 CH 9.6 Apply the Law of Cosines.notebook
6
August 30, 2013
Apply the Law of Cosines
Which law would you use: Sines or Cosines?
359
25oxo
Pull
Pull
SINES
Apply the Law of Cosines
Which law would you use: Sines or Cosines?
4
1719
Pull
Pull
COSINES
Apply the Law of CosinesHeron's Area Formula
The area of any triangle can be found with the formula:
where
Apply the Law of Cosines
Find the area of the triangle:
7
9
4
Apply the Law of Cosines Apply the Law of Cosines
Algebra 2 CH 9.6 Apply the Law of Cosines.notebook
7
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