Introduction to Trigonometry

1. Introduction to Trigonometry 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. Topic 1 Labeling Right Triangles

4. 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 oppositeside • theadjacentside

5. 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...

6. B C A Labeling Right Triangles • Before you label the other two sides you must have a reference angleselected. • It can be either of the two acute angles. • In the triangle below, let’s pick angle B as the reference angle. This will be our reference angle...

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

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

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

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

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. B hypotenuse C (ref. angle) A

13. Labeling Right Triangles • However, side AB is now the side oppositesince it is across from angle C. B opposite hypotenuse C (ref. angle) A

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

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

16. W X Y 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.

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

18. R T S Labeling Practice • Given that angle R is the reference angle, label the triangle’s sides. • Click to see the correct answers.

19. R T S Labeling Practice • The answers are shown below: hypotenuse adjacent opposite

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