**Trigonometry**

**Opposite**

**Adjacent**

**Hypotenuse**

30º

θ

SOH CAH TOA

Sin 30°=

Cos 30°=

Tan 30°=

Sine Cosine Tangent

**4**

**12**

**10**

4/12

10/12

4/10

30º

18

x

opp

adj

hyp

Sin30º=x/18

18 x Sin30º= x/18

.'. x= 18 x sin30º

.'. x= 9

x

12

40º

Cos 40º = x/12

12 x Cos40º= x/12

.'.x= 12x Cos40º

.'. x= 9.2

adj

hyp

x

8.4

Tan32º= x/8.4

8.4 x Tan32º= x/8.4

.'. x = Tan32ºx 8.4

.'. x = 5.25

32º

Sin= opp/hyp

Cos= adj/hyp

Tan= opp/adj

opp/hyp

adj/hyp

opp/adj

**Lets learn**

trigonometry

trigonometry

Problem for you!

3

x

Find x

Did you get...

38°

A mountain is 3km high on one side but how tall is it on the other?

Get a pen and paper to work this out

Tan(38°)= x/3

3x Tan38= x/3

x=3 x Tan38

.'. x = 2.34km

Therefore, the other side of

the mountain is 2.34km.

the side opposite the angle

the side next to the angle

the longest side

the angle of the triangle

John is standing 7 meters away from a tree. The length from the top of the tree to his feet is 11 meters away.

How tall is the tree?

7m

11m

44°

Woohoo!

Good Job!

The Answer is...

Sin44°= x/11

.'.x= 11x Sin44°

.'.x= 7.6m

.'. the Tree is 7.6m tall

not to actual size

The bike and the car are leaving the city but at different speeds. After 1 hour the distance between the city and the bike is 54km away. The angle is 29 degrees. How far away is the bike from the car?

Question no. 3

x

54

19

x

37°

Example: Finding a side

Cos37°= 19/x

19÷ Cos37= 19/x

.'. x= 19÷ Cos37

.'. x= 23.8

*if the x is at the top of the fraction then you have to multiply

*if the x is at the bottom then you have to divide

SOH CAH TOA

Multiply

Divide

Find X

Find X

Find x

Tips

29

ANSWER..........

Cos29°= 54/x

.'. x= 54 ÷ Cos29°

.'. x= 61.74 km

Finding a Side of a right angled

Triangle using Trigonometry

hmmmm

Trigonometry

Finding the angle of this triangle is easy... try this...

12m

15m

You use Tan because you have the opposite and adjacent measurements.

Tan0 = 12/15

Tanˉ (12÷15)

.'. x= 38.7mˉθ

0

Finding the Angle

Question!

What is the Angle?

0

145

100