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Introduction to

Trigonometry

Right Triangle Trigonometry

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Introduction

Trigonometry is a branch of mathematics

that uses triangles to help you solve

problems. Trig is useful to surveyors, engineers,

navigators, and machinists (and others

too.)

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Labeling RightTriangles

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Labeling Right Triangles

The most important skill you need right

now is the ability to correctly label the

sides of a right triangle.

The names of the sides are:

the

hypotenuse

the

opposite

side

the

adjacent

side

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Labeling Right Triangles

The hypotenuse is easy to locate because

it is always found across from the right

angle.

Here is the

right angle...

Since this side is

across from the right

angle, this must be

the hypotenuse.

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Labeling Right Triangles

Before you label the other two sides you

must have a reference angle selected.

It can be eitherof the two acute angles.

In the triangle below, lets pick angle B as

the reference angle.

A

B

C

This will be our

reference angle...

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Labeling Right Triangles

Remember, angle B is our reference

angle.

The hypotenuse is side BC because it isacross from the right angle.

A

B (ref. angle)

C

hypotenuse

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Labeling Right Triangles

Side AC is across from our reference

angle B. So it is labeled: opposite.

A

B (ref. angle)

C

opposite

hypotenuse

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Labeling Right Triangles

The only side unnamed is side AB. This

must be the adjacentside.

A

B (ref. angle)

C

adjacent hypotenuse

opposite

Adjacent means beside ornext to

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Labeling Right Triangles

Lets put it all together.

Given that angle B is the reference angle,

here is how you must label the triangle:

A

B (ref. angle)

C

hypotenuse

opposite

adjacent

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Labeling Right Triangles

Given the same triangle, how would the

sides be labeled if angle C were the

reference angle? Will there be any difference?

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Labeling Right Triangles

Angle C is now the reference angle.

Side BC is still the hypotenuse since it is

across from the right angle.

A

B

C (ref. angle)

hypotenuse

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Labeling Right Triangles

However, side AB is now the side

opposite since it is across from angle C.

A

B

C (ref. angle)

opposite hypotenuse

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Labeling Right Triangles

That leaves side AC to be labeled as

the adjacentside.

A

B

C (ref. angle)

adjacent

hypotenuseopposite

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Labeling Right Triangles

Lets put it all together.

Given that angle C is the reference

angle, here is how you must label thetriangle:

A

B

C (ref. angle)

hypotenuseopposite

adjacent

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Labeling Practice

Given that angle X is the reference angle,

label all three sides of triangle WXY.

Do this on your own. Click to see theanswers when you are ready.

W X

Y

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Labeling Practice

How did you do?

Click to try another one...

W X

Y

hypotenuse

opposite

adjacent

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Labeling Practice

Given that angle R is the reference angle,

label the triangles sides.

Click to see the correct answers.R

ST

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Labeling Practice

The answers are shown below:

R

ST

hypotenuse

opposite

adjacent

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Which side will never be the reference angle?

What are the labels?

Hypotenuse, opposite, and adjacent

The right angle