Labeling Trigonometry Triangles
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Trigonometry, derived from the Greek words for 'triangle' and 'measurement', focuses on the study of triangles, particularly right-angled ones. In a right triangle, the longest side is the hypotenuse, while the other sides are referred to as opposite and adjacent relative to a given angle θ (theta). The presentation emphasizes the labeling of these sides for clarity in understanding trigonometric relations.
Labeling Trigonometry Triangles
- 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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