Trigonometric Ratios in Right Triangles

Trigonometric Ratios are based on the Concept of Similar Triangles!

All 45º- 45º- 90º Triangles are Similar!

45 º

2

2

22

45 º

1

1

2

45 º

1

2

1

2

1

All 30º- 60º- 90º Triangles are Similar!

1

60º

30º

½

23

32

60º

30º

2

4

2

60º

30º

1

3

All 30º- 60º- 90º Triangles are Similar!

10 60º

30º

5

35

2 60º

30º1

3

160º

30º 21

23

Naming Sides of Right Triangles

We will be learning 3 trig ratios

Sine- Abbreviation is Sin (but you pronounce it Sign, not Sin!!!)

Cosine- Abbreviation is Cos

Tangent- Abbreviation is Tan

Adjacent

OppositeTan

hypotenuse

AdjacentCos

hypotenuse

oppositeSin

The Trigonometric Ratios(The SOHCAHTOA model)

A little trick to help you remember…

Some Old Horse, Caught Another Horse,

Taking Oats Away

Find the value of each of the trigonometric functions of the angle

Adjacent

12 13

c = Hypotenuse = 13

b = Opposite = 12

a

b

c

Adjacent = 5

Opposite =

Hypotenuse =

12

13

In order to use your calculator to find trigonometric ratios, it MUST be in degree mode!!!!

Hint: Before taking ANY test that might have trig on it, change the mode to Degree to be safe (EOC, ACT, Semester Exam…)

Use a calculator to find each value. Round to the nearest ten thousandth.

135tan

104cos

42sin

Solving a Problem withthe Tangent Ratio

60º

53 ft

h = ?

We know the angle and the We know the angle and the side adjacent to 60º. We want to side adjacent to 60º. We want to know the opposite side. Use theknow the opposite side. Use thetangent ratio:tangent ratio:

ft 92353

531

3

5360tan

h

h

h

adj

opp

1

2 3

Why?