Transcript Introduction to Trigonometry

Introduction to
Trigonometry
Right Triangle Trigonometry
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.)

Labeling Right
Triangles
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
Labeling Right Triangles

The hypotenuse is easy to locate because
it is always found across from the right
angle.
Since this side is
across from the right
angle, this must be
the hypotenuse.
Here is the
right angle...
Labeling Right Triangles
Before you label the other two sides you
must have a reference angle selected.
 It can be either of the two acute angles.
 In the triangle below, let’s pick angle B as
This will be our
the reference angle. B
reference angle...

A
C
Labeling Right Triangles
Remember, angle B is our reference
angle.
 The hypotenuse is side BC because it is
across from the right angle.

B (ref. angle)
hypotenuse
A
C
Labeling Right Triangles

Side AC is across from our reference
angle B. So it is labeled: opposite.
B (ref. angle)
hypotenuse
A
C
opposite
Labeling Right Triangles
Adjacent means beside or next to
 The only side unnamed is side AB. This
must be the adjacent side.
B (ref. angle)
adjacent
hypotenuse
C
A
opposite
Labeling Right Triangles
Let’s put it all together.
 Given that angle B is the reference angle,
here is how you must label the triangle:

B (ref. angle)
hypotenuse
adjacent
C
A
opposite
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?

Labeling Right Triangles
Angle C is now the reference angle.
 Side BC is still the hypotenuse since it is
across from the right angle.

B
hypotenuse
A
C (ref. angle)
Labeling Right Triangles

However, side AB is now the side
opposite since it is across from angle C.
B
opposite
hypotenuse
A
C (ref. angle)
Labeling Right Triangles

That leaves side AC to be labeled as
the adjacent side.
B
hypotenuse
opposite
A
C (ref. angle)
adjacent
Labeling Right Triangles
Let’s put it all together.
 Given that angle C is the reference
angle, here is how you must label the
triangle:

B
hypotenuse
opposite
C (ref. angle)
A
adjacent
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 the
answers when you are ready.

W
Y
X
Labeling Practice
How did you do?
 Click to try another one...

W
adjacent
opposite
hypotenuse
Y
X
Labeling Practice
Given that angle R is the reference angle,
label the triangle’s sides.
 Click to see the correct answers.

R
T
S
Labeling Practice

The answers are shown below:
R
hypotenuse
adjacent
T
opposite
S
Which side will never be the reference angle?
The right angle
What are the labels?
Hypotenuse, opposite, and adjacent