Law of Cosines

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Law of Cosines

• Section 6.2

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Learning Goal

• I will be able to solve a triangle.

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Why?

• Solving triangles is an important part of
  surveying and navigation.

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Remember The Law of Sines
The Law of Sines works best in solving oblique
triangles when we are given 2 angles and 1 side
(AAS or ASA) or in solving oblique triangles when
we are given 1 non-included angle and 2 sides
(SSA) although this leads to the ambiguous case.
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Section 6.2, Law of Cosines, pg. 401
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Example 1
X
given SAS
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Example 2
Solve triangle ABC if a 5, b 7 and c 6.
To avoid confusion, use the Law of Cosines to
find the angle opposite the longest side.
given SSS
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Example 3
Solve triangle ABC if a 1, b 5 and c 8.
Ha Ha!
Remember to check to see if a triangle can be
made.
No Triangle
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Example 4
In triangle ABC, AB 5, BD 2, DC 4 and CA
7. Find AD.
In triangle ABD and triangle ABC, angle B is the
same.
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All together then
2nd angle
LoS
LoC
Largest Angle
Geometry
3rd angle
LoS
2nd angle
LoC
Geometry
3rd Side
3rd angle
2nd side
LoS
Geometry
LoS
3rd angle
remaining side
LoS
remaining angle
LoS
Geometry
2nd angle
remaining side
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Learning Goal

• I will be able to solve a triangle.

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End of Notes.

• Homework p. 405 1, 3, 9, 11, 13, 15, 17, 25,
  27, 29