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MAP4C
College and Apprenticeship Math
MAP4C Lesson Outline
Text: Mathematics 12: College & Apprenticeship Mathematics
Unit 1:
Section Pre-Test
Do questions:
1 (a, c), 2 (a, c, e), 3, 4(a), 5 (b)
6 (a, d), 7, 8
(page 4)
(page 5)
Read:
Review:
Ratio and Proportion
The Pythagorean Theorem
Approximate Numbers and Significant Digits
(pages 6 - 7)
(page 8 – 10)
(pages 10 – 12)
Section 1.1 – Determining Lengths of Sides in Right Angles
Read: Page 13-17
Sin, Cos, Tan (SOH CAH TOA)
February 2014
Page 1
MAP4C
College and Apprenticeship Math
Section 1.1
Do questions: Practice A: (1, 2, 3) (Page 17)
Practice B: (4, 6, 7, 9. 10, 12, 13 ) (pages 18, 19, 20)
How to find the missing angle of a right triangle using the sine ratio.
Example 2
Find A.
Solution
O
Sin A =
H
Section 1.2:
Determining the Measures of Angles in Right Triangles
Read: Pages 21 – 24
Do Questions:
February 2014
Practice A:
Practice B:
1, 2, 3, 4 (page 24)
6, 7 (a, b), 9 (a, c), 12, 14, 15 (pages 25-28)
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MAP4C
College and Apprenticeship Math
Section 1.3:
the Sine Law in Acute Triangles
The sine law is the relationship between the ratios of the sines of the angles of a triangle
and the lengths of the opposite sides.
For the triangle given below:
The Sine Law can be written as:
Sin A Sin B Sin C
a
b
c


or


a
b
c
Sin A Sin B Sin C
Recognizing when to use the Sine Law.
You need:


an angle and the value of its side opposite
a second angle and the need to find its unknown opposite side


an angle and the value of its side opposite
a second side and the need to find its unknown opposite angle
OR
February 2014
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MAP4C
College and Apprenticeship Math
Example 1
Calculate the Sin values for degrees
x (.4067)   8 (.6293) 

x (.4067)
8 (.6293) 

.4067
.4067 
5.0345 
.4067 
x  12.4
x
Read: Pages 29 – 34
Do Questions:
February 2014
Practice A:
Practice B:
1, 3 (page 35)
4, 5, 8, 9 (a, c), 10, 11, 12 (pages 35-37)
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MAP4C
Section 1.4:
College and Apprenticeship Math
The Trigonometric Ratios of Obtuse Angles
Read: Pages 39 – 41
Do Questions:
Section 1.5:
Practice A:
Practice B:
1 (a, c, d, h, l), 2 (page 42)
4, 5, 7, 8, 12 (a) (pages 42 and 43)
The Cosine Law
The cosine law is used to find the third side of a triangle when two sides and a
contained angle are known or to find an angle measure when the length of three sides are
known.
The contained angle in a triangle is the angle between the two given sides of the triangle.
In the example given below C is the contained angle between the sides CA and CB.
The Cosine Law states that for a ΔABC :
c 2  a2  b2  2ab CosC
b2  a2  c 2  2ac CosB
a2  b2  c 2  2bc CosA
February 2014
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MAP4C
College and Apprenticeship Math
Example 1
Find the missing side shown in the diagram below using the cosine law.
Solution
a 2  b 2  c 2  2bc CosA
a 2  (16) 2  (11) 2  2(16)(11) CosA
Example 1 cont.
So the missing length is 23.3 units long.
Example 2
Find the angle A using the cosine law.
February 2014
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MAP4C
College and Apprenticeship Math
Solution
First using algebra manipulate the formula to isolate Cos A.
a 2  b 2  c 2  2bc CosA
a 2 - b 2  c 2  2bc CosA
a 2 - b 2  c 2  2bc CosA

 2bc
 2bc
a2 - b2  c 2
 CosA
 2bc
c 2  b2 - a2
CosA 
2bc
Read: Pages 44 – 46
Do Questions:
Section 1.6:
Practice A:
Practice B:
1, 3 (page 47)
4, 5, 7, 9, 11, 12, 16 (pages 47 and 49)
Exercises
Do Questions:
February 2014
1, 5 (page 53), 7 (page 54), 12 (page 55)
Page 7