

8-5/8-6
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Mathematics
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10th Grade
•
Easy
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14 Slides • 22 Questions
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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.
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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.
5
Multiple Choice
6
Multiple Choice
7
Multiple Choice
8
Multiple Choice
9
Multiple Choice
10
Multiple Choice
11
Multiple Choice
12
Multiple Choice
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THETA
θIn 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. :)
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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.
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SINE
Sine is abbreviated "sin" and is pronounced "sign."
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Multiple Choice
Find sin C. Remember...side opposite <C/hypotenuse
14/48
48/50
14/50
48/14
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Multiple Choice
Select the correct ratio for SinA (opposite/hypotenuse)
3537
3512
3735
3712
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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.
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COSINE
Cosine is abbreviated as cos.
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Multiple Choice
Find cos D. Remember...side adjacent to <D / hypotenuse
4/3
3/4
3/5
4/5
21
Multiple Choice
Find cos E
3/5
4/5
3/4
1/4
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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.
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TANGENT
Tangent is abbreviated tan.
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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
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Multiple Choice
26
Multiple Choice
27
Multiple Choice
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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 40o will have the same ratio of opposite/hypotenuse. This means, the sine of that 40o angle will always be the same.
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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.
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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 40o. Do you get 0.6427876? On the last few questions, you will be asked to find sin/cos/tan of angles.
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Multiple Choice
tan (30) ≈
0.176
0.268
0.364
0.577
32
Multiple Choice
cos (34o) = ?
1.10943235
0.4551023
0.8290376
33
Multiple Choice
tan (10) ≈
0.176
0.268
0.364
0.577
34
Multiple Choice
tan (45) ≈?
(Think about why this makes total sense)
0.839
1
1.192
1.428
35
Multiple Choice
sin (89o) = ?
0.9998477
0.0293144
0.4550325
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Multiple Choice
LAST QUESTION...Which of the three ratios can be greater than 1?
sine
cosine
tangent
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