8-5/8-6

8-5/8-6

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RIGHT TRIANGLE VOCABULARY

When you studied 45-45-90 and 30-60-90 triangles, you learned special vocabulary to refer to the different side lengths. For example, in a 30-60-90 triangle there is a short leg, long leg, and a hypotenuse.

Vocab

For the rest of this unit, we are going to use the terms OPPOSITE, ADJACENT, and HYPOTENUSE to identify the different side lengths of a right triangle. When using opposite and adjacent, it is important to understand which angle you are using. In this picture, the word opposite and adjacent refer to the sides opposite and adjacent to angle A.

Multiple Choice

From ∠D, what side is DO?

• Adjacent
• Hypotenuse
• Opposite

Multiple Choice

From ∠D, what side is DG?

• Adjacent
• Hypotenuse
• Opposite

Multiple Choice

From ∠A, what side is AB?

• Adjacent
• Hypotenuse
• Opposite

Multiple Choice

From ∠A, what side is AC?

• Adjacent
• Hypotenuse
• Opposite

Multiple Choice

From ∠A, what side is BC?

• Adjacent
• Hypotenuse
• Opposite

Multiple Choice

From ∠C, what side is AC?

• Adjacent
• Hypotenuse
• Opposite

Multiple Choice

From ∠C, what side is BC?

• Adjacent
• Hypotenuse
• Opposite

Multiple Choice

From ∠C, what side is AB?

• Adjacent
• Hypotenuse
• Opposite

THETA 

 $\theta$  

In mathematics, the lowercase θ is used as a variable to represent an angle. It's just a variable; don't get worked up about it. :)

SINE

The sine of an angle is defined as the ratio of the length of the side opposite an acute angle to the length of the hypotenuse.

SINE

Sine is abbreviated "sin" and is pronounced "sign."

Multiple Choice

Find sin C. Remember...side opposite <C/hypotenuse

• 14/48

• 48/50

• 14/50

• 48/14

Multiple Choice

Select the correct ratio for SinA (opposite/hypotenuse)

• $\frac{37}{35}$

• $\frac{12}{35}$

• $\frac{35}{37}$

• $\frac{12}{37}$

COSINE

The cosine of an angle is defined as the ratio of the length of the side adjacent to an acute angle to the length of the hypotenuse.

COSINE

Cosine is abbreviated as cos.

Multiple Choice

Find cos D. Remember...side adjacent to <D / hypotenuse

• 4/3

• 3/4

• 3/5

• 4/5

Multiple Choice

Find cos E

• 3/5

• 4/5

• 3/4

• 1/4

TANGENT

The tangent of an angle is defined as the ratio of the length of the side opposite an acute angle to the length of the side adjacent to the angle.

TANGENT

Tangent is abbreviated tan.

Multiple Choice

Find the tan Z. Remember, this equals the side length opposite <Z divided by the side length adjacent <Z

• 35/21

• 21/28

• 35/28

• 28/21

Multiple Choice

• 32/40
• 40/24
• 32/24
• 24/32

Multiple Choice

• 27/36
• 27/45
• 45/36
• 45/27

Multiple Choice

• A
• B
• C
• D

USING YOUR CALCULATOR

Remember, all triangle with the same three angle measures will be similar and therefore have the same ratios of side lengths. For example, all triangles with a right angle and a 40^o will have the same ratio of opposite/hypotenuse. This means, the sine of that 40^o angle will always be the same.

USING YOUR CALCULATOR

Your calculator has been programmed to calculate the ratios of side lengths for the acute angles of all right triangles. Find the sin/cos/tan button(s) on your calculator.

USING YOUR CALCULATOR

Let's see if you found it. Sometimes it requires you to first push the "shift" or "2nd" key. Type in sin 40^o. Do you get 0.6427876? On the last few questions, you will be asked to find sin/cos/tan of angles.

Multiple Choice

tan (30) ≈

• 0.176

• 0.268

• 0.364

• 0.577

Multiple Choice

cos (34^o) = ?

• 1.10943235

• 0.4551023

• 0.8290376

Multiple Choice

tan (10) ≈

• 0.176

• 0.268

• 0.364

• 0.577

Multiple Choice

tan (45) ≈?

(Think about why this makes total sense)

• 0.839

• 1

• 1.192

• 1.428

Multiple Choice

sin (89^o) = ?

• 0.9998477

• 0.0293144

• 0.4550325

Multiple Choice

LAST QUESTION...Which of the three ratios can be greater than 1?

• sine

• cosine

• tangent