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MBF3C
Unit 3 - Foundations for College Mathematics
Lesson Eleven: Trigonometry Ratios




Label parts of a right triangle i.e. opposite, adjacent and hypotenuse
Recognize parts of a right triangle i.e. opposite, adjacent and hypotenuse
Using the trigonometry ratios to find unknown sides of a right triangle
Using the trigonometry ratios to find unknown interior angles of a right triangle
Trigonometry: The Sine Ratio
The sine ratio can be used calculate an unknown angle or and unknown side in a right
triangle.
To find the either of these unknowns the opposite side and hypotenuse are used from
an angle of reference.
Example
Suppose we use A as the angle of reference then:
Sine always used the hypotenuse and opposite sides of a right triangle.
Sine Opposite Hypotenuse: SOH
When  A is an acute angle in a right triangle, then
Sin A =
Length of side Opposite angle A
Length of Hypotenuse side
Sin A =
Opposite
Hypotenuse
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Unit 3 - Foundations for College Mathematics
How to find the missing side of a right triangle using the sine ratio.
Example 1
Find the value of x.
Solution
Sin A =
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O
H
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Unit 3 - Foundations for College Mathematics
Support Questions
1.
In each triangle, name the side:
a. opposite E
2.
b. the hypotenuse
Calculate the Sin A and Sin B in each triangle.
a.
3.
Calculate.
a. Sin 35
4.
b.
b. Sin 71
c. Sin 55
d. Sin 90
Calculate the value of x.
a.
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b.
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Unit 3 - Foundations for College Mathematics
Support Questions (con’t)
c.
d.
How to find the missing angle of a right triangle using the sine ratio.
Example 2
Find A.
Solution
O
Sin A =
H
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Unit 3 - Foundations for College Mathematics
Support Questions
5.
Calculate.
a. Sin 1 0.725
6.
c. Sin 1
3
7
d. Sin 1
5
12
Calculate E to the nearest degree.
a. Sin E = 0.625
7.
b. Sin 1 0.325
b. Sin E = 0. 812
c. Sin E =
3
5
d. Sin E =
7
11
Calculate E.
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Unit 3 - Foundations for College Mathematics
Trigonometry: The Cosine Ratio
The cosine ratio can be used calculate an unknown angle or and unknown side in a
right triangle.
To find the either of these unknowns the adjacent side and hypotenuse are used from
an angle of reference.
Example
Suppose we use A as the angle of reference then:
Cosine always used the hypotenuse and adjacent sides of a right triangle.
Cosine Adjacent Hypotenuse: CAH
When  A is an acute angle in a right triangle, then
Cos A =
Length of side Adjacent angle A
Length of Hypotenuse side
Cos A =
Adjacent
Hypotenuse
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Unit 3 - Foundations for College Mathematics
How to find the missing side of a right triangle using the Cosine ratio.
Example 3
Find the value of x.
Solution
Cos A =
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A
H
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Unit 3 - Foundations for College Mathematics
Support Questions
8.
In each triangle, name the side:
a. adjacent  E
9.
b. adjacent  Y
Calculate the Cos A and Cos B in each triangle.
a.
10.
Calculate.
a. Cos 35
11.
b.
b. Cos 71
c. Cos 55
d. Cos 90
Calculate the value of x.
a.
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b.
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Unit 3 - Foundations for College Mathematics
Support Questions (con’t)
c.
d.
How to find the missing angle of a right triangle using the Cosine ratio.
Example 4
Find C.
Solution
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Unit 3 - Foundations for College Mathematics
Support Questions
12.
Calculate.
a. Cos 1 0.725
13.
c. Cos 1
3
7
d. Cos 1
5
12
Calculate E to the nearest degree.
a. Cos E = 0.625
14.
b. Cos 1 0.325
b. Cos E = 0. 812
c. Cos E =
3
5
d. Cos E =
7
11
Calculate E.
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Unit 3 - Foundations for College Mathematics
Trigonometry: The Tangent Ratio
The Tangent ratio can also be used calculate an unknown angle or and unknown side in
a right triangle.
To find the either of these unknowns the adjacent side and opposite sides are used
from an angle of reference.
Example
Suppose we use A as the angle of reference then:
Tangent always used the opposite and adjacent sides of a right triangle.
Tangent Opposite Adjacent: TOA
When  A is an acute angle in a right triangle, then
Tan A =
Length of side opposite angle A
Length of Adjacent side
Tan A =
Opposite
Adjacent
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Unit 3 - Foundations for College Mathematics
How to find the missing side of a right triangle using the Tangent ratio.
Example 5
Find the value of x.
Solution
Tan A =
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A
H
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Unit 3 - Foundations for College Mathematics
Support Questions
15.
In each triangle, name the side:
a. adjacent  F
16.
b. opposite  Y
Calculate the Tan A and Tan B in each triangle.
a.
17.
Calculate.
a. Tan 35
18.
b.
b. Tan 71
c. Tan 55
d. Tan 90
Calculate the value of x.
a.
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b.
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Unit 3 - Foundations for College Mathematics
Support Questions
c.
d.
How to find the missing angle of a right triangle using the Cosine ratio.
Example 6
Find A.
Solution
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Unit 3 - Foundations for College Mathematics
Support Questions
19.
Calculate.
a. Tan 1 0.725
20.
c. Tan 1
3
7
d. Tan 1
5
12
Calculate E to the nearest degree.
a. Tan E = 0.625
21.
b. Tan 1 0.325
b. Tan E = 0. 812
c. Tan E =
3
5
d. Tan E =
7
11
Calculate E.
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Unit 3 - Foundations for College Mathematics
Key Question #11
1.
In each triangle, name the side:
2.
Calculate the Sin A and Sin B in each triangle.
3.
Calculate.
a. Sin 42
4.
b. Cos 68
c. Tan 12
Calculate the value of x.
a.
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b.
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Unit 3 - Foundations for College Mathematics
Key Question #11 (con’t)
5.
Calculate.
a. Sin 1 0.612
6.
b. Cos 1 0.825
c. Cos 1
2
5
d. Tan 1
3
13
Calculate E to the nearest degree.
a. Sin E = 0.387
b. Sin E = 0. 900
c. Cos E =
12
29
d. Tan E =
13
5
7.
Calculate  E.
8.
A guy wire is 13.5 m long. It supports a vertical power pole that is 8.7 m tall.
Calculate the distance between where the guy wire is anchored into the ground
from the base of the power pole.
?
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Unit 3 - Foundations for College Mathematics
Key Question #11 (con’t)
9.
A 5.0 m ladder is leaning 3.7 m up a wall. What is the angle the
ladder makes with the ground?
10.
A kite has a string 100 m long anchored to the ground. The string
makes and angle with the ground of 68. What is the horizontal
distance of the kite from the anchor?
11.
A ladder is leaned 10 m up a wall with its base 6 m from the wall. What angle
does the ladder make with the ground?
12.
The acronym SOHCAHTOA is often used in trigonometry. What do you think
each letter stands for and give an example finding either an unknown side or an
unknown angle using a portion of this acronym.
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Unit 3 - Foundations for College Mathematics
Lesson Twelve: Law of Sines





drawing a labelling triangle angles and sides
interpreting information and drawing diagrams based on that information
using the sine law to find an unknown side in a triangle
using the sine law to find an unknown side in a triangle
drawing diagrams and solving questions, using the Sine Law, involving the angle
of elevation and depression
Trigonometry: The Sine Law
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:


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an angle and the value of its side opposite
a second angle and the need to find its unknown opposite side
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Unit 3 - Foundations for College Mathematics
OR


an angle and the value of its side opposite
a second side and the need to find its unknown opposite angle
Example 1
x Sin24   8 Sin39 

x Sin24
8 Sin39 

Sin24 
Sin24 
8 Sin39 
Sin24 
x  12.4
x
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Unit 3 - Foundations for College Mathematics
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Support Questions
1.
Given each of the ratios below, state whether the unknown angle will be larger or
smaller than the one given.
a.
2.
Sin 67 Sin X

13
7.2
b.
Sin Y Sin 81

7.6
8.4
c.
Sin 37 Sin A

4
8
Given each of the ratios below, state whether the unknown angle will be larger or
smaller than the one given.
a.
Sin 55 Sin 71

13
x
b.
Sin 16 Sin 77

12.5
y
c.
Sin 83 Sin 41

a
7.2
3.
Find the length of the indicated side.
4.
Find the measure of angle A.
5.
In  PQR, find the value of q, if R = 73, Q = 32, and r = 23 cm.
6.
In  ABC, find the value of c, if A = 52, C = 47, and a = 12 m.
7.
In  TUV, find the value of U, if T = 37, u = 16 cm, and t = 22 cm.
8.
In  XYZ, find the value of Z, if X = 72, x = 41 m, and z = 11 m.
9.
A radio tower is supported by two wires on opposite sides. The wires form an
angle of 60 at the top of the post. On the ground, the ends of the wire are 15 m
apart, and one wire is at a 45 angle to the ground. How long will the wires be?
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Unit 3 - Foundations for College Mathematics
Key Question #12
1.
Given each of the ratios below, state whether the unknown angle will be larger or
smaller than the one given.
a.
2.
Sin B Sin 35

10
5.1
b.
Sin Y Sin 64

9.1
8.4
c.
Sin 37 Sin A

6.1
3.8
Given each of the ratios below, state whether the unknown angle will be larger or
smaller than the one given.
a.
Sin 13 Sin 52

8
x
b.
Sin 54 Sin 23

12.5
y
c.
Sin 17 Sin 76

a
7.2
3.
Find the length of the indicated side.
4.
Find the measure of angle C.
5.
In  TUV, find the value of t, if T = 61, U = 24, and u = 17 cm.
6.
In  EFG, find the value of e, if F = 52, G = 47, and f = 40 m.
7.
In  ABC, find the value of A, if B = 37, a = 10 cm, and b = 17 cm.
8.
In  QRS, find the value of Q, if S = 72, q = 26 m, and s = 35 m.
9.
An architect designs a house that is 10 m wide. The rafters
holding up the roof are equal length and meet at an angle of
65. The rafters extend 0.4 m beyond the supporting wall. How
long are the rafters?
10.
Does the sine law apply to right triangles? Explain your answer.
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Unit 3 - Foundations for College Mathematics
Lesson Thirteen: Law of Cosine




drawing a labelling triangle angles and sides
interpreting information and drawing diagrams based on that information
using the cosine law to find an unknown side in a triangle
using the cosine law to find an unknown side in a triangle
Trigonometry: 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
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Unit 3 - Foundations for College Mathematics
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.
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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
Example 2 cont.
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Support Questions
1.
Find the length of the indicated side.
2.
Find the measure of angle X.
3.
In  PQR, find the value of r, if p = 13 cm, q = 8 cm and R = 63.
4.
In  ABC, find the value of a, if b = 17 cm, c = 28 cm and A = 105.
5.
In  TUV, find the value of U, if v = 10 cm, u = 16 cm, and t = 22 cm.
6.
In  XYZ, find the value of Z, if x = 41 m, y = 32 m, and z = 28 m.
7.
The bases on a softball diamond are 15 m apart. A player picks up a fair
ground ball 3 m from third base, along the line from second to third base.
How far must he throw it to first base?
8.
Find the measure, to the nearest degree, of the middle angle in a triangle
that has side lengths of 8 cm, 19 cm, and 21 cm.
9.
A plane leaves Hamilton and flies due east for 75 km. At the same time, a
second plane flies in a direction 40 southeast for 120 km. How far apart are the
planes when they reach their destinations?
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Unit 3 - Foundations for College Mathematics
Key Question #13
1.
Find the length of the indicated side.
2.
Find the measure of angle C.
3.
In  EFG, find the value of f, if e = 7.1 cm, g = 8.9 cm and F = 71.
4.
In  LMO, find the value of m, if o = 34 cm, l = 62 cm and M = 98.
5.
In  BCD, find the value of B, if b = 46 cm, c = 70 cm, and d = 58 cm.
6.
In  ABC, find the value of C, if a = 5.2 m, b = 3.8 m, and c = 6.7 m.
7.
Two paths diverge at a 48 angle. Two mountain bike riders take
separate routes at 8 km/hr and 12 km/hr. How far apart are they after 2
hours? Include a diagram.
8.
Draw a diagram to solve this problem: Oshawa is 10 km due east of Ajax.
Uxbridge is 18 km NW of Oshawa. How far is it from Ajax to Uxbridge? Explain
whether you have enough information to solve this problem.
9.
A golfer hits a tee shot on a 325 m long straight golf hole. The
ball is hooked (hit at an angle) 18 to the left. The ball lands
185 m from the tee. How far is the ball from the hole?
10.
Given the points A(0, 0), B(3, 1) and C(1, 4), what is the
measure of  ABC?
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Unit 3 - Foundations for College Mathematics
Lesson Fourteen: Trigonometry and Problem Solving

Identifying the trigonometry strategy needed to solve various real life situations
Trigonometry Strategies
One of the most important strategies to solve the question is to draw a diagram and fill
as much information as possible. Often more that one strategy can be used to solve
such questions. The strategy shown or suggested is considered the most direct or
logical route but not necessarily the only.
Example
A telephone pole and an electrical pole are 200 metres away from each other. From a
point halfway between the two poles the angle of elevation of their tops is 8 and 12 .
How tall are the poles?
Solution
First draw the diagram to help organize the information given.
Since the diagram contains two right angle triangles then SOHCAHTOA can be used to
solve the question.
Pole 1
x
Tan 8 
100
100 Tan8  x
14.5  x
Pole 2
x
100
100 Tan12  x
21.3  x
Tan 12 
 the two poles are approximately 14.5 m and 21.3 m tall.
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Unit 3 - Foundations for College Mathematics
Example 2
The edges of a tooth are 1.1 cm and 0.8 cm long. The base of the tooth is 0.6 cm long.
Determine the angle at which the edges meet.
Solution
Draw the diagram and label appropriately.
There are no angles given for the triangle but all three sides are present. To find an
angle when no other angles are present the Law of Cosine will need to be used.
2
2
2

1.1  0.8   0.6
Cos 
2(1.1)(0.8)
Cos  0.847
  Cos 1 (0.847)
  32
Support Questions
1.
Two buildings are 38 m apart. From the top of the shorter building, the angle of
elevation of the top of the taller building is 31 and the angle of depression of the
base is 40 . Determine the height of each building.
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Unit 3 - Foundations for College Mathematics
Support Questions (con’t)
2.
The area of a triangle is given by the formula
A
base  height .
2
Determine the area
of the triangle given below.
3.
Calculate the height of the building in the diagram given below.
4.
Two chains support a weight at the same point. The chains are attached to the
ceiling and are 6.0 m and 5.5 m in length. The angle between the chains is
105 . How far apart are the chains at the ceiling?
Key Question #14
1.
Noah and Brianna want to calculate the distance between
their houses which are opposite sides of a water park.
They mark a point, A, 150 m along the edge of the water
park from Brianna’s house. The measure NBA as 80
and BAN as 75 . Determine the distance between their
houses.
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Unit 3 - Foundations for College Mathematics
Key Question #14 (con’t)
2.
From an observation tower that overlooks a small lake, the angles of depression
of point A, on one side of the lake, and point B, on the opposite side of the lake
are, 7 and 13 , respectively. The points and the tower are in the same vertical
plane and the distance from A to B is 1 km. Determine the height of the tower.
3.
A children’s play area is triangular. The sides of the play area measure 100m,
250m and 275m respectively. Calculate the area of the play area.
4.
A baseball diamond is a square with sides 27.4 m. The pitcher’s mound is 18.4
m from home plate on the line joining home plate and second base. How far is
the pitcher’s mound from first base?
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Unit 3 - Foundations for College Mathematics
Lesson Fifteen: Creating Nets

Use of nets to transform 2 dimensional drawings into 3 dimensional figures
Nets
A lot of 3 dimensional objects are created from flat material. Cardboard boxes and
sheet metal in duct work are two such examples. Material is cut, and bent or folded to
form objects.
Example
Draw one example of a net that would produce a cube.
Solution
Support Questions
1.
Below are examples of nets. Which will produce closed objects? Explain why
the others will not.
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Unit 3 - Foundations for College Mathematics
Key Question #15
1.
For each of the nets given below draw another net that will produce the same
object.
2.
Create a net for each of the object given below
3.
Identify the patterns that will produce a closed 3-dimensional object when folded.
Explain your reasoning.
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Unit 3 - Foundations for College Mathematics
Unit 3 – Support Question Answers
Lesson 11
1.
a. FG
b. YZ
2.
a. SinA 
3.
a. 0.574
4.
a.
3 .7
1 .5
; SinB 
4
4
b. SinA 
b. 0.946
c. 0.819
x
18
x  18 Sin 23
x  7.03 cm
Sin 23 
c.
d.
4
x
4  x Sin 48
13.3
x
13.4  x Sin 62
Sin 48 
Sin 62 
4
x Sin 48

Sin 48
Sin 48
4
x
Sin 48
5.38  x
13.4
x Sin 62

Sin 62
Sin 62
13.4
x
Sin 62
15.2  x
5.
a. 46
b. 19
6.
Sin1 0.625
a.
 39
Sin1 0.812
b.
 54
c.
a.
b.
c.
SinE 
2 .1
3 .7
E  Sin1
E  35
8.
a. GE
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d. 1
b.
x
Sin 37 
3 .7
x  3.7 Sin 37
x  2.23 cm
7.
12
13.4
; SinB 
18
18
SinE 
2 .1
3 .7
c. 25
10
18
E  Sin1
Sin1
3
5
d.
4
9
E  Sin1
E  34
7
d.
11
 40
Sin 1
 37
SinE 
10
18
d. 25
E  26
13.4
16.1
13.4
E  Sin1
16.1
E  56
SinE 
4
9
b. XY
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Unit 3 - Foundations for College Mathematics
1.5
3.7
; CosB 
4
4
a. CosA 
10.
a. 0.819
b. 0.326
c. 0.574
d. 0
11.
a.
b.
c.
d.
x
3.7
x  3.7 Cos 37
x  2.95 cm
a. 44
13.
a.
14.
a.
2 .1
CosE 
3.7
E  Cos 1
15.
a. FG
16.
a. TanA 
17.
a. 0.700
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Cos 62 
4
x Cos 48

Cos 48
Cos 48
4
x
Cos 48
5.98  x
13.4
xCos 62

Cos 62
Cos 62
13.4
x
Cos 62
28.5  x
b. 71
2 .1
3.7
b.
c. 65
Cos1 0.812
 36
c.
Cos 1
d. 65
3
5
c.
10
CosE 
18
4
CosE 
9
10
18
E  56
d.
Cos 1
7
11
 50
 53
b.
E  Cos 1
13.3
x
13.4  x Cos 62
Cos 48 
Cos 23 
Cos 1 0.625
 51
E  55
4
x
4  x Cos 48
x
18
x  18 Cos 23
x  16.57 cm
Cos 37 
12.
b. CosA 
13.4
12
; CosB 
18
18
9.
d.
E  Cos 1
E  64
13.4
16.1
13.4
E  Cos 1
16.1
E  34
CosE 
4
9
b. XZ
3 .7
1 .5
; TanB 
1.5
3.7
b. 2.90
b. TanA 
12
13.4
; TanB 
13.4
12
c. 1.43
d. undefined (error)
Page 36
MBF3C
18.
Unit 3 - Foundations for College Mathematics
a.
b.
c.
18
x
18  x Tan 23
d.
Tan 23 
x
3.7
x  3.7 Tan 37
x  2.79 cm
Tan 37 
19,
a. 36
20.
a.
21.
18
x Tan 23

Tan 23
Tan 23
18
x
Tan 23
42.4  x
b. 18
Tan 1 0.625
 32
a.
Tan 1 0.812
 39
E  60
E  Tan 1
c.
Tan 1
d. 23
3
5
d.
E  61
E  Tan 1
E  66
7
11
d.
9
TanE 
4
18
10
Tan 1
 32
 31
c.
18
TanE 
10
3 .7
2 .1
Tan 62 
c. 23
b.
3 .7
TanE 
2 .1
E  Tan 1
b.
x
13.4
x  13.4 Tan 62
x  25.2 cm
x
4
x  4 Tan 48
x  4.44 m
Tan 48 
16.1
13.4
16.1
E  Tan 1
13.4
E  50
TanE 
9
4
Lesson 12
1.
a. 7.2 < 13 so X is smaller than 67
c. 8 > 4 so A is larger than 37
b. 7.6 < 8.4 so Y is smaller than 81
2.
a. 71 > 55 so x is larger than 13
c. 83 > 41 so a is larger than 7.2
b. 77 > 16 so y is larger than 12.5
3.
Sin54 Sin27

x
8
8 Sin54  x Sin27
8 Sin54 x Sin27

Sin27
Sin27
8 Sin54
x
Sin27
14.3  x
MBF3C
Page 37
MBF3C
Unit 3 - Foundations for College Mathematics
4.
SinA Sin26

6.7
3.2
6.7 Sin26  3.2 SinA
6.7 Sin26 3.2 SinA

3.2
3.2
6.7 Sin26
 Sin A
3.2
0.9178  Sin A
sin-1 0.9178  A
66.6   A
5.
Sin32 Sin73

q
23
23 Sin32  q Sin73
23 Sin32 q Sin73

Sin73
Sin73
23 Sin32
q
Sin73
12.7  q
6.
Sin47 Sin52

c
12
12 Sin47  c Sin52
12 Sin47 c Sin52

Sin52
Sin52
12 Sin47
c
Sin52
11.1  c
MBF3C
Page 38
MBF3C
Unit 3 - Foundations for College Mathematics
7.
SinU Sin37

16
22
16 Sin37  22 SinU
16 Sin37 22 SinU

22
22
16 Sin37
 Sin U
22
0.4377  Sin U
sin-1 0.4377  U
26  U
8.
SinZ Sin72 

11
41
11 Sin72   41 SinZ
11 Sin72  41 SinZ

41
41
11 Sin72 
 Sin Z
41
0.255  Sin Z
sin -1 0.255  Z
15.0  Z
9.
Sin60 Sin45

15
x
15 Sin45  x Sin60
15 Sin45 x Sin60

Sin60
Sin60
15 Sin45
x
Sin60
12.2  x
Sin60 Sin75

15
y
15 Sin75  y Sin60
15 Sin75 y Sin60

Sin60
Sin60
15 Sin75
y
Sin60
16.7  y
the lengths of the wires are 12.2 m and 16.7 m
MBF3C
Page 39
MBF3C
Unit 3 - Foundations for College Mathematics
Lesson 13
1.
x 2  30 2  50 2  2(30)(50)C os100
x 2  3920.9
x  62.6
2.
35 2  17 2  28 2
2(35)(17)
CosX  0.6134
CosX 
X  Cos 1 0.6134
X  52.2 
3.
r 2  13 2  8 2  2(13)(8)Co s63
r 2  138.57
r  11.8 cm
4.
a 2  17 2  28 2  2(17)(28)C os105
a 2  1319.4
a  36.3 cm
5.
10 2  22 2  16 2
2(10)(22)
CosU  0.7455
CosU 
U  Cos 1 0.7455
U  41.8 
6.
412  32 2  28 2
2(41)(32)
CosZ  0.732
CosZ 
Z  Cos 1 0.732
Z  42.9 
MBF3C
Page 40
MBF3C
Unit 3 - Foundations for College Mathematics
7.
x 2  12 2  15 2  2(12)(15)C os90
x 2  369
x  19.2
8.
8 2  212  19 2
2(8)(21)
CosX  0.4286
CosX 
X  Cos 1 0.4286
X  64.6 
9.
x 2  75 2  120 2  2(75)(120) Cos40
x 2  6237
x  78.97 km
Lesson 14
1.
A
38
A  38 Tan 40
A  31.88m
Tan 40 
B2
38
B2  38 Tan 31
B2  22.83m
Tan 31 
Therefore Building A is 31.88 m tall and Building two is 54.71 m tall
(22.83+31.88)
MBF3C
Page 41
MBF3C
Unit 3 - Foundations for College Mathematics
2.
h
7.8
h  7.8 Sin 39
h  4.9 cm
Sin 39 
Area 
bh (13.8)( 4.9) 67.62


 33.81 cm 2
2
2
2
3.
s
75
s  75 Tan 45
s  75 m
Tan 45 
H
75
H  75 Tan 61
H  135.3 m
Tan 61 
MBF3C
Page 42
MBF3C
Unit 3 - Foundations for College Mathematics
4.
x 2  6 2  5.5 2  2(6)(5.5)C os105
x 2  83.33
x  9.1 m
Lesson 15
1.
Net A is closed and will produce a square based pyramid.
Net B is closed and will produce a rectangular prism.
Net C is not closed the edges of partial circle (arc) needs to be straight to go
around the edges of the complete circle given in the net.
Net D is closed and will produce a cylinder.
Net E is closed and will produce a triangular prism.
MBF3C
Page 43