1. Trigonometry
SOH CAH TOA

2. Theta θ
Theta is a variable used for angle measure. It will be used as the reference angle when doing trigonometry. θ

3. Theta θ
Example: Find the measure of θ
65˚ θ
55˚

4. Theta θ
In this case, theta is 60˚.
65˚ θ
55˚

5. Theta θ
Θ is just another symbol used as a variable and to represent unknowns (similar to x and y.)

6. Naming Sides of a Triangle
The side opposite the right angle is always the hypotenuse.
Hypotenuse

7. Naming Sides of a Triangle
The side opposite the reference angle (in this case θ) is the opposite side.
Opposite

8. Naming Sides of a Triangle
The remaining side is the adjacent side. Adjacent means “close to.”
Adjacent

9. Naming Sides of a Triangle
All together we have:
Hypotenuse
Opposite
Adjacent

10. Naming Sides of a Triangle
Notice how the Adjacent and Opposite sides change when the reference angle θ changes, but the Hypotenuse is always the same.
Hypotenuse
Adjacent
Opposite

11. Trigonometry
Definition: a branch of mathematics dealing with the properties of triangles and their applications.
Specifically, we will be dealing with the ratios sine, cosine, and tangent

12. sine
The sine of an angle is equal to the length of the opposite side divided by the length of the hypotenuse.
“sin” is the button you use on your calculator to use this ratio.
Hypotenuse
Opposite
Adjacent

13. cosine
The cosine of an angle is equal to the length of the adjacent side divided by the length of the hypotenuse.
“cos” is the button you use on your calculator to use this ratio.
Hypotenuse
Opposite
Adjacent

14. tangent
The tangent of an angle is equal to the length of the opposite side divided by the length of the adjacent side.
“tan” is the button you use on your calculator to use this ratio.
Hypotenuse
Opposite
Adjacent

15. SOH, CAH, TOA
“SOH CAH TOA” is a mnemonic device used to help you remember these ratios. Just like “Please Excuse My Dear Aunt Sally.”

16. SOH CAH TOA
SOH
CAH
TOA
Hypotenuse
Opposite
Adjacent

17. Examples
Find the hypotenuse of this triangle.
77 in
35˚

18. Examples
Find the side opposite to θ if θ = 59˚
66 mi θ

19. Examples
You want to break into a museum by scaling the wall with rope. You know the top of the museum is at a 47˚ to your feet when you are standing 25 ft. away. How many feet of rope do you need?
Opp.
47˚
25 ft.

20. Remember SOH CAH TOA only works for right triangles.
Your calculator must be in degree mode if you are entering degrees for theta.