1Press Ctrl-APress Ctrl-A

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IntroductionIntroduction

Applied MathematicsPreliminary Stage 6

2

ClickClickHypotenuse

Hypotenuse

Op

posit

eO

pp

osit

eA

dja

cen

tA

dja

cen

t

OppositeOppositeAdjacentAdjacent

HypotenuseHypotenuse – always oppositeopposite the right-angleright-angle.

OppositeOpposite – always oppositeopposite the markedmarked angle.angle.

AdjacentAdjacent – always next-tonext-to the marked anglemarked angle.

3

aa

bb

cc

ccWhich is the Hypotenuse?Which is the Hypotenuse?

4

yy

zz

xx

xxWhich is the Hypotenuse?Which is the Hypotenuse?

5

pp

rr

qq

qqWhich is the Hypotenuse?Which is the Hypotenuse?

6

nngg

mmWhich is the Opposite?Which is the Opposite?

mm

7

nngg

mmWhich is the Opposite?Which is the Opposite?

nn

8

nngg

mm

Which is the Adjacent?Which is the Adjacent?nn

9

nngg

mm

Which is the Adjacent?Which is the Adjacent?mm

10

θθ

1313

1212

55

Opposite Opposite θθ ::

Adjacent Adjacent θθ ::

HypotenuseHypotenuse ::1313

55

1212

11

θθ

55

44

33

Opposite Opposite θθ ::

Adjacent Adjacent θθ ::

HypotenuseHypotenuse ::55

44

33

12

13

Hypotenuse

Hypotenuse

Op

posit

eO

pp

osit

e

OppositeOpposite

ClickClick

Sin Sin θθ = =OppositeOppositeHypotenuseHypotenuse

θθ

θθ

TrigRatios

14

1313

1212

Sin Sin θθ = =OppositeOppositeHypotenuseHypotenuse

PP

QQ RR

55

Sin P =Sin P =12121313 Sin R =Sin R = 55

1313 TrigRatios

15

66

3030oo

mmsin 30sin 30oo = =mm

666x6x x6x6

m =m =66 xx sinsin 3030oo

= 3= 3Use yourCalculator!

TrigRatios

Sin Sin θθ = =OppositeOppositeHypotenuseHypotenuse

16

17

Hypotenuse

Hypotenuse

AdjacentAdjacent

Ad

jacen

tA

dja

cen

tClickClick

Cos Cos θθ = =AdjacentAdjacentHypotenuseHypotenuse

θθ

θθ

TrigRatios

18

1313

1212

Cos Cos θθ = =AdjacentAdjacentHypotenuseHypotenuse

PP

QQ RR

55

Cos P =Cos P = 551313 Cos R =Cos R =1212

1313 TrigRatios

19

666060oo Cos Cos θθ = =AdjacentAdjacent

HypotenuseHypotenuse

mm coscos 6060oo = =mm66

6x6x x6x6

m =m =66 xx coscos 6060oo

= 3= 3

Use yourCalculator!

TrigRatios

20

21

Op

posit

eO

pp

osit

e

AdjacentAdjacent

Ad

jacen

tA

dja

cen

tClickClick

Tan Tan θθ = =OppositeOppositeAdjacentAdjacent

θθ

θθOppositeOpposite

TrigRatios

22

1313

1212

Tan Tan θθ = =OppositeOppositeAdjacentAdjacent

PP

QQ RR

55

Tan P =Tan P =121255

Tan R =Tan R = 551212

TrigRatios

23

66 3030oo

mm TanTan 3030oo = =mm66

6x6x x6x6

m =m =66 xx TanTan 3030oo

≈ ≈ 3.463.46

Use yourCalculator!

To 2 decimalplaces

TrigRatios

Tan Tan θθ = =OppositeOppositeAdjacentAdjacent

24

25

TrigRatios

How high is the Empire State Building in NYC

78 metres

h

80o

tan 80o = h

78

h =

x7878x

78 x tan 80o

= 442 metres

26

TrigRatios

How much rope is needed for a flying fox over the lake?

d

40 m

60o tan 60o = d

40

h =

x4040x

40 x tan 60o

= 70 metres