Labeling Triangles for Trigonometry. How to label a Right Triangle before applying Trigonometry to it.

1. Image Source: www.tributehomes.com.au

2. The “Trigonometry” mathematics of Triangles is used
extensively in Building and Architecture.
Image Source: http://www.infoteli.co

3. The "Trigon" part of "Trigonometry" refers to a three sided
geometrical shape, eg, a Triangle.
Trigon = 3 sides, Hexagon = 6 sides, Octagon = 8 sides, etc.
The "metry" part of "Trigonometry" refers to the activity of measuring.
So the word "Trigonometry" means :
Measurements of the Sides and Angles in Triangles.
The full story on Trigonometry actually extends beyond Triangles:
Trigonometry is a branch of mathematics which deals with triangles,
circles, waves and oscillations.
However, we will only be looking at Triangles in this Presentation.

4. Basic Trigonometry only works for Right Angled Triangles.

5. The Angle in a Right Triangle is not called “x” or “y”, but is
assigned the special Greek letter Ѳ which is called “theta”.
Other letters used are “phi” φ , “alpha” α , and “beta” β
Ѳ
o

6. The Hypotenuse or “HYP” or just “H” is the
LONGEST SIDE of the Right Triangle.
It is the long sloping side opposite the Right Angle.
Ѳ
o

7. The Opposite or “OPP” or just “O” is the
SIDE of the Right Triangle opposite the angle Ѳ
We call it the “Rocket Opposite” eg. Think of where
a rocket launched from the Ѳ would hit the Triangle.
Ѳ
o
Opposite-OPP-O

8. The Adjacent or “ADJ” or just “A” is the
SIDE of the Right Triangle next to the angle Ѳ
The Adjacent runs between θ and the right angle.
Ѳ
o
Adjacent - ADJ - A

9. We recommend labeling the Triangle in the following order:
“Hypotenuse” longest side first, then do the “Rocket Opposite”,
and finally label the “Adjacent” as the side running in between
the slope angle θ and the 90 degree Right Angle.
Ѳ
o
Adjacent - ADJ - A
Opposite-OPP-O

10. We can also label the Triangle for the other Angle as follows:
“Hypotenuse” longest side first, then do the “Rocket Opposite”,
and finally label the “Adjacent” as the side running in between
the slope angle θ and the 90 degree Right Angle.
β
o
Opposite - OPP - O
Adjacent-ADJ-A

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