This document introduces right triangle trigonometry and labeling the sides of a right triangle. It explains that the hypotenuse is always opposite the right angle, while the opposite and adjacent sides depend on the reference angle. The reference angle can be either acute angle, and changing the reference angle switches the labels of the opposite and adjacent sides. Practice problems are included to help label triangles given a reference angle.

1. Introduction toIntroduction to
TrigonometryTrigonometry
Right Triangle Trigonometry

2. 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.)

3. Labeling Right
Triangles

4. Labeling Right Triangles
 The most important skill you need rightThe most important skill you need right
now is the ability to correctly label thenow is the ability to correctly label the
sides of a right triangle.sides of a right triangle.
 The names of the sides are:The names of the sides are:
 thethe hypotenusehypotenuse
 thethe oppositeopposite sideside
 thethe adjacentadjacent sideside

5. 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.

6. 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
the reference angle.
A
B
C
This will be our
reference angle...

7. Labeling Right Triangles
 Remember, angle B is our reference
angle.
 The hypotenuse is side BC because it is
across from the right angle.
A
B (ref. angle)
C
hypotenuse

8. Labeling Right Triangles
 Side AC is across from our reference
angle B. So it is labeled: opposite.
A
B (ref. angle)
C
opposite
hypotenuse

9. Labeling Right Triangles
 The only side unnamed is side AB.
This must be the adjacent side.
A
B (ref. angle)
C
adjacent
hypotenuse
opposite
Adjacent means beside or next to

10. 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:
A
B (ref. angle)
C
hypotenuse
opposite
adjacent

11. 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?

12. 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

13. 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

14. Labeling Right Triangles
 That leaves side AC to be labeled as
the adjacent side.
A
B
C (ref. angle)
adjacent
hypotenuse
opposite

15. 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:
A
B
C (ref. angle)
hypotenuse
opposite
adjacent

16. 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 X
Y

17. Labeling Practice
 How did you do?
 Click to try another one...
W X
Y
hypotenuse
opposite
adjacent

18. Labeling Practice
 Given that angle R is the reference angle,
label the triangle’s sides.
 Click to see the correct answers.
R
ST

19. Labeling PracticeLabeling Practice
 The answers are shown below:
R
ST
hypotenuse
opposite
adjacent

20. Which side will never be the reference angle?
What are the labels?
Hypotenuse, opposite, and adjacentHypotenuse, opposite, and adjacent
The right angleThe right angle