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Cosine Law (Solutions).notebook
1
January 06, 2016
Mar 58:46 AM
Cosine Law
Jan 42:52 PM
A
B Ca
bc
Labelling any oblique triangle:
Angles are CAPITAL LETTERS.Sides are lowercase letters.
IMPORTANT: The side opposite an angle is given the same letter (just a lowercase letter!)
So far we've only been able to use trigonometry for right angled triangles.
In order to use trigonometry for oblique triangles (no right angles) you must use 1 of 2 laws.
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Cosine Law (Solutions).notebook
2
January 06, 2016
Aug 2112:20 PM
For any triangle, the following equations are true:
A
B
Ca
bc
c2 = a2 + b2 2ab Cos(C)
b2 = a2 + c2 2ac Cos(B)
a2 = b2 + c2 2bc Cos(A)
These three equations are examples of the cosine law.
Aug 228:15 AM
When to use the Cosine Law:
SAS (sideangleside)
and you need to find a side
SSS (sidesideside)
and you need to find any angle
s
sA
s
s s
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Cosine Law (Solutions).notebook
3
January 06, 2016
Sep 1410:54 AM
Example 1: Determine the length of a to the nearest metre.
A
B
C
32m
40m
58o
Sep 1410:54 AM
Example 2: Determine the length of c to the nearest tenth of a cm.
A
C 73o
12.3cm
14.9cmB
![Page 4: Cosine Law (Solutions).notebookkillornmath.weebly.com/uploads/3/0/9/5/30958945/cosine_law.pdf · Cosine Law (Solutions).notebook 5 January 06, 2016 Sep 142:46 PM B A 12.3 10.5C 13.2](https://reader036.vdocuments.mx/reader036/viewer/2022062604/5fb9a29145dd5d093a1be781/html5/thumbnails/4.jpg)
Cosine Law (Solutions).notebook
4
January 06, 2016
Oct 164:01 PM
p. 136137
# 1, 2, 4, 6a
Sep 171:12 PM
Example 3: Determine the measure of angle D to the nearest degree.
D
E
θ 80
100
95 F
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Cosine Law (Solutions).notebook
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January 06, 2016
Sep 142:46 PM
B
A C
12.3 10.5
13.2
θ
Example 4: Determine the measure of angle B to the nearest tenth of a degree.
Oct 164:16 PM
Example 5: Solve the following triangle
a=11 b=5 C=20o
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Cosine Law (Solutions).notebook
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January 06, 2016
Aug 228:57 AM
pg. 136
# 3, 5, 6c, 7a
pg. 171
# 3c, 4b, 8