trigonometry soh cah toa. theta θ theta is a variable used for angle measure. it will be used as...

Trigonometry SOH CAH TOA

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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.

Theta θ

Example:

Find the measure of θ

65˚

55˚

Theta θ

In this case, theta is 60˚.

65˚

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

Hypotenuse

The side opposite the right angle is always the hypotenuse.

Page 7: 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

Naming Sides of a Triangle

Opposite

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

Page 8: 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

Naming Sides of a Triangle

Adjacent

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

Page 9: 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

Naming Sides of a Triangle

Hypotenuse

Adjacent

Opposite

All together we have:

Page 10: 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

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

Page 12: 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

sine

Hypotenuse

Oppositesin

Hypotenuse

Adjacent

Opposite

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.

Page 13: 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

cosine

Hypotenuse

Adjacent

Opposite

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

Adjacentcos

Page 14: 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

tangent

Hypotenuse

Adjacent

Opposite

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.

Adjacent

Oppositetan

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

Adjacentcos

Adjacent

Oppositetan

Hypotenuse

Oppositesin

Hypotenuse

Adjacent

Opposite

Page 17: 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

Examples

Find the hypotenuse of this triangle.

35˚

77 in

Page 18: 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

Examples

Find the side opposite to θ if θ = 59˚

66 mi

Page 19: 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

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?

25 ft.

47˚

Opp.

Page 20: 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

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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