Basic Trigonometry

Parts of a Right Triangle

AAdjacent SideC

Opposite Side

BHypotenuse

Imagine that you are at Angle A looking

into the triangle.

The adjacent side is the side next to Angle A.

The opposite side is the side that is on the opposite side of the triangle from Angle A.

The hypotenuse will always be the longest side, and opposite from the right angle.

Parts of a Right Triangle

AAdjacent SideC

Opposite Side

BHypotenuse

Now imagine that you move from Angle A to Angle B.

From Angle B the adjacent side is the side next to Angle B.

From Angle B the opposite side is the side that is on the opposite side of the triangle.

ReviewHypotenuse

Hypotenuse

Opposite Side

Adjacent SideA

B

For Angle A

This is the Opposite Side

This is the Adjacent Side

For Angle B

AThis is the Adjacent Side

This is the Opposite Side

Opposite Side

Adjacent Side

B

Trig Ratios

We can use the lengths of the sides of a right triangle to form ratios. There are 3 different ratios that we can make. Adjacent

OppositeHypotenuse

AC

B

OppositeHypotenuseAdjacentHypotenuseOppositeAdjacent

Using Angle A to name the sides

Use Angle B to name the sides

The ratios are still the same as before!!

Trig Ratios• Each of the 3 ratios has a name• The names also refer to an angle

OppositeSine of Angle A =Hypotenuse

AdjacentCosine of Angle A =Hypotenuse

OppositeTangent of Angle A =Adjacent

Hypotenuse

Adjacent

OppositeA

Trig Ratios

B

Opposite=Hypotenuse

Adjacent =Hypotenuse

Opposite =Adjacent

Hypotenuse

Adjacent

OppositeA

If the angle changes from A to BThe way the ratios are made is the same

B

B

B

Cosine of Angle

Sine of Angle

Tangent of Angle

SOHCAHTOA

AdjacentA

B

OppositeHypotenuse

Here is a way to remember how to make the 3 basic Trig Ratios

1) Identify the Opposite and Adjacent sides for the appropriate angle

2) SOHCAHTOA is pronounced “Sew Caw Toe A” and it means

Sin is Opposite over Hypotenuse, Cos is Adjacent over Hypotenuse, and Tan is Opposite over Adjacent

Put the underlined letters to make

SOH-CAH-TOA

Examples of Trig Ratios

Sin P

Cos P

1220

16Q

P

Tan P Tan Q

Cos Q

Sin Q1620

1220

1612

1220

1620

1216

First we will find the Sine, Cosine andTangent ratios for Angle P.

Next we will find the Sine, Cosine, andTangent ratios for Angle Q

Opposite

Adjacent

Remember SohCahToa

Similar Triangles and Trig Ratios

ABC QPR

35

4A

B

1220

16

Q

P

R

C

They are similar triangles, since ratios of corresponding sides are the sameLet’s look at the 3 basic Trig ratios for these 2 triangles

Tan Q

Cos Q

Sin Q1220

1620

1216

Tan A

Cos A

Sin A35

45

34

Notice that these ratios are equivalent!!

Similar Triangles and Trig Ratios

• Triangles are similar if the ratios of the lengths of the corresponding side are the same.

• Triangles are similar if they have the same angles

• All similar triangles have the same trig ratios for corresponding angles