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Trigonometry SOH CAH TOA

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

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

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

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

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**Naming Sides of a Triangle**

The side opposite the right angle is always the hypotenuse. Hypotenuse

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**Naming Sides of a Triangle**

The side opposite the reference angle (in this case θ) is the opposite side. Opposite

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**Naming Sides of a Triangle**

The remaining side is the adjacent side. Adjacent means “close to.” Adjacent

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**Naming Sides of a Triangle**

All together we have: Hypotenuse Opposite Adjacent

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**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

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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

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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

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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

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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

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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.”

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SOH CAH TOA SOH CAH TOA Hypotenuse Opposite Adjacent

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

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

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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.

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**Remember SOH CAH TOA only works for right triangles.**

Your calculator must be in degree mode if you are entering degrees for theta.

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