Download lessons 9.7 and 9.8.notebook

lessons 9.7 and 9.8.notebook
April 29, 2016
Lessons 9.7 and 9.8: Trigonometric Ratios
Objective: students will use trigonometric ratios to find unknown lengths of right triangles. Apr 28­8:49 PM
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lessons 9.7 and 9.8.notebook
April 29, 2016
Key Vocabulary
trigonometric ratios: a ratio of the lengths of two sides of a right triangle.
tangent (acute angle of right triangle): the ratio of the length of the side opposite the angle to the side adjacent to the angle
sine (acute angle of right triangle): the ratio of the length of the side opposite the angle to the length of the hypothenuse cosine (acute angles of a right triangle): the ratio of the length of the side adjacent to the length of the hypothenuse
Apr 28­8:52 PM
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lessons 9.7 and 9.8.notebook
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Apr 28­9:20 PM
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lessons 9.7 and 9.8.notebook
April 29, 2016
Example 1: Finding the Tangent Ratio
For ABC. find the tangent of angle B
B
36
C
hypothenuse
85
77
A
Apr 28­9:00 PM
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lessons 9.7 and 9.8.notebook
April 29, 2016
Checkpoint
B
36
C
For ABC. find the tangent of angle A
hypothenuse
85
77
A
Apr 28­9:05 PM
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lessons 9.7 and 9.8.notebook
April 29, 2016
Example 2: Using Calculators to Find the Tangent
a. tan 18 b. tan 45
Apr 28­9:08 PM
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lessons 9.7 and 9.8.notebook
April 29, 2016
Checkpoint
tan 35
tan 10
Apr 28­9:12 PM
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lessons 9.7 and 9.8.notebook
April 29, 2016
Example 3: Using Tangent Ratio
When the sun's rays strike the moon's surface at an angle of 6 , the edge of a lunar crater casts a shadow that has a length of about 4700 meters. What is the depth of the crater?
Apr 28­9:11 PM
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lessons 9.7 and 9.8.notebook
April 29, 2016
Example 4: Finding the Sine and Cosine Ratio
Find the sine and cosine of angle L.
J
8
K
17
15
L
Apr 28­9:15 PM
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lessons 9.7 and 9.8.notebook
April 29, 2016
Checkpoint
J
8
K
Find the sine and cosine of angle J
17
15
L
Apr 28­9:21 PM
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lessons 9.7 and 9.8.notebook
April 29, 2016
Example 5: Using a Calculator to Find Sine and Cosine
a. sin 38
b. cos 43
Apr 28­9:22 PM
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lessons 9.7 and 9.8.notebook
April 29, 2016
Checkpoint
Approximate sin 74 and cos 12
Apr 28­9:26 PM
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lessons 9.7 and 9.8.notebook
April 29, 2016
Example 6: Using Cosine Ratio F
Use the Cosine Ratio to find the unknown length
16
41
E
x
D
Apr 28­9:27 PM
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lessons 9.7 and 9.8.notebook
April 29, 2016
Example 7: Using a Sine Ratio
Use the sine ratio to find the unknown length.
164
x
27
Apr 28­9:34 PM
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