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Module 3-1

Trigonometry made simple

Trigonemtry is a very important subject

and the principles are widely applied in

many other subjects. Therefore, the

importance of understanding it cannot be

understated and if you can understand it

you will be able to apply its principles in

these other related subjects

Trigonometry made simple

Canadian

Swans

Prefer

Small

Insects

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Trigonometry made simple

Convert to triangles

Sum of all angles

Pythagorus

SOHCAHTOA

Inverse SOHCAHTOA

Step One

Right lets do some examples, convert this

into right angle triangles

Step One

This one is simple just draw a line here

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Step One

Convert this into right angle triangles

Step One

Simple again

Step One

Convert shape into right angle triangles

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Step One

Well this has to be converted into 6 right

angle triangles

Step One

Convert this shape into triangles

Step One

This converts to 6 right angled triangles

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Step Two

Sum of all angles = 180 x (N – 2)

Where N = number of sides of polygon

Lets do some examples

Step Two

Determine the sum of all the angles in

this polygon

Step Two

Well a triangle has 3 sides

180 x (3 – 2) = 180 x 1 = 180o

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Step Two

Determine the sum of all the angles in

this polygon

Step Two

Well a triangle has 3 sides

180 x (3 – 2) = 180 x 1 = 180o

Step Two

80o

70o

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Step Two

80o

70o

30o

Step Two

55o

55o

Step Two

That covers triangles now lets move

onto four sided shape, what is the

missing angle.

Lets apply the rule

180 x (N -2) = 180 X ( 4-2) = 180 X 2

= 360 degrees

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Step Two

We know 3 of the angles

125 + 85 + 80 = 290

360 – 290 = 70 degrees

The missing angle is 70 degrees

Step Two

85o

125o

80o

70o

Step Two

Now this rule applies to all polygons

What about this shape here

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Step Two

80o

160o

110o120o

Step Two

Lets move onto step 3 pythagrous

• In mathematics, the Pythagorean

theorem or is a relation in geometry

among the three sides of a right

triangle (right-angled triangle).

Step Two

• In terms of areas, it states:

• In any right-angled triangle, the

area of the square whose side is the

hypotenuse (the side opposite the

right angle) is equal to the sum of

the areas of the other two sides

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Trigonometry

a2 + b2 = c2

TrigonometryB

CA

3cm5cm

4cm

Adjacent

Op

po

site

Module 3-2

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B

CA

8cm

6.5cm

AdjacentO

pp

osi

te

a

b

c

Module 3-3

Example 2

B

CA

5cm

Adjacent

Op

po

site

a

7cm

c

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Module 3-4

Example 3

B

CAcm

cm

Adjacent

Op

po

site

a

b

c

Module 3-5

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Example 4

B

CA10cm

12cm

AdjacentO

pp

osi

te

a

b

c

Module 3-6

Sine Wave

1 90o 180o 270o 360o

-1

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Cosine Wave

1 90o 180o 270o 360o

-1

Tangent Wave

1 90o 180o 270o 360o

-1

Trigonometry

45o

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Trigonometry

Op

po

site

45o

Trigonometry

Adjacent45o

Trigonometry

A

6cm

45oWhich function

should you

apply

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Trigonometry

A

5cm

45oWhich function

should you

apply

Trigonometry

A5cm

45oWhich function

should you

apply

Module 3-7

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Example 1

B

A

5cm

38o

Sine Wave

1 90o 180o 270o 360o

-1

0.62

38o

Module 3-8

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Example 2

B

CA

12cm

42o

c

AdjacentO

pp

osi

te

Module 3-9

Example 3

B

CA

23cm

52o

c

Adjacent

Op

po

site

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Module 3-10

Example 4

B

CA

8cm70o

c

Opposite

Ad

jace

nt

Module 3-11

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Example 5

B

CA

5cm70o

Opposite

Ad

jace

nt

Module 3-12

SOHCAHTOA

Sin -1

Cos -1

Tan -1

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Example 6

B

C

A

5cm

OppositeA

dja

cen

t

13cm

Module 3-13

Example 7

B

C

A

9cm

Opposite

Ad

jace

nt

19.6cm

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Module 3-14

Example 8

B

CA

10cm

Adjacent

Op

po

site30cm

Module 3-15

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Exercise 1

11m

700

Exercise 1

Calculate the height of a building

when a 11m ladder is pitched to the

roof at an angle of 70 degrees?

Module 3-16

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Exercise 2

13.5m

750

Exercise 2

Calculate the distance from the

building when a 13.5m ladder is

pitched against a building at an angle

of 75 degrees?

Module 3-17

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Exercise 3

Two ladders are pitched together s

shown here. One ladder is 11m and

the other is 13.5m and they make an

angle of 95 degrees, determine the

height to point A ?

Exercise 3

13.5m950

11m

A

B600C

Module 3-18

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Exercise 5

Two ladders 13.5m and 9m are pitched

against a vertical wall so as to make

angles of 50 degrees

How much higher is the head of the

longer ladder?

Exercise 5

13.5m

B

500

500

9m

a

Module 3-19

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Exercise 6

A 30m turntable ladder is fully

extended. At what angle must it be

elevated to reach a window 23m from

the ground. (The bottom of the ladder

is 1.5m from the ground)

30m

23m

1.5m

Module 3-20

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Exercise 7

A ladder 10m from building A reaches

a window 8m up. When you turn it

over through 90 degrees it reaches a

window 11.5m high on the other side.

How wide is the street and how long

is the ladder?

Exercise 7

8m

B

11.5m

900

A B

10m