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Introduction to Introduction to TrigonometryTrigonometry
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 The most important skill you need right now is the ability to correctly label the now 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: the the hypotenusehypotenuse the the opposite opposite sideside the the adjacentadjacent side side
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.
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...
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
Labeling Right Triangles
Side AC is across from our reference angle B. So it is labeled: opposite.
A
B (ref. angle)
Copposite
hypotenuse
Labeling Right Triangles
The only side unnamed is side AB. This must be the adjacent side.
A
B (ref. angle)
C
adjacenthypotenuse
opposite
Adjacent means beside or next to
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
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.
A
B
C (ref. angle)
hypotenuse
Labeling Right Triangles
However, side AB is now the side opposite since it is across from angle C.
A
B
C (ref. angle)
oppositehypotenuse
Labeling Right Triangles
That leaves side AC to be labeled as the adjacent side.
A
B
C (ref. angle)adjacent
hypotenuseopposite
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)
hypotenuseopposite
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 X
Y
Labeling Practice
How did you do? Click to try another one...
W X
Y
hypotenuse
opposite
adjacent
Labeling Practice
Given that angle R is the reference angle, label the triangle’s sides.
Click to see the correct answers.R
ST
Labeling PracticeLabeling Practice
The answers are shown below:
R
ST
hypotenuse
opposite
adjacent
Which side will never be the reference angle?
What are the labels?
Hypotenuse, opposite, and adjacentHypotenuse, opposite, and adjacent
The right angleThe right angle
