Trigonometry SOH CAH TOA

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

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

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

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

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

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

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

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

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

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

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

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

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

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.”

SOH CAH TOA SOH CAH TOA Hypotenuse Opposite Adjacent

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

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

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.

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