Download 6.5 Law of Cosines

6.5
The Law of Cosines applies to all Non-right-angled triangles.
Example: In triangle ABC, AB=11, AC=7 and angle A=28.
Find the length of BC to 1 decimal place.
C
1. Draw a diagram.
2. Break the triangle into 2 right triangles.
3. Identify new variables.
4. Write two equations using Pythagoras’
Theorem.
5. Simplify the system of equations.
6. Use trigonometry to write an
equation for x.
7. Solve for x and sub into the first
equation.
8. Use calculator and find the value of
a.
A
B
Applying the Law of Cosines
Finding an Angle Using the Law of Cosines
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Find the measure of angle A.
Using the calculator:
Set angle mode to degrees and enter
(612 + 432 - 382) ÷ (2 x 61 x 43) =
Then press: [COS-1] [ANS] [ )] [ENTER]
Finding an Angle Using the Law of Cosines
Given triangle DEF, find E.
Pg. 498
#3,4,5ac,7,10
MC 1,2