UNIT 3: RIGHT TRIANGLE TRIGONOMETRY Vocabulary Builder
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UNIT 3: RIGHT TRIANGLE TRIGONOMETRY
Vocabulary Builder
Similar Triangles Square RootHypotenuse
legSimplest radical
form Variable
Pythagorean Theorem
45-45-90 Triangles 30-60-90 Triangles
UNIT 3: RIGHT TRIANGLE TRIGONOMETRY3.1 Trigonometric Ratios
Square rootPerfect Square
Radical expressionradicand
Perfect Square
5 8 14
30 18 23
𝟔 𝟐 2 𝟔 3 𝟏𝟏
10 𝟑 3 𝟏𝟎 𝟓 𝟑
right triangle
equals
hypotenuse
Side lengths
42 + 82 = 𝑥2
16 + 64 = 𝑥2
80 = 𝑥2
4 5 = 𝑥
8.9 = 𝑥
62 + 32 = 𝑥2
36 + 9 = 𝑥2
45 = 𝑥2
3 5 = 𝑥
6.7 = 𝑥
𝑥2 + 3.92 = 112
𝑥2 + 15.21 = 121
𝑥2 = 95.79
𝑥 = 9.75
32 + 102 = 𝑥2
9 + 100 = 𝑥2
109 = 𝑥2
10.44 = 𝑥
72 + 22 = 𝑥2
49 + 4 = 𝑥2
53 = 𝑥2
7.3 = 𝑥
𝑥2 + 3.62 = 7.42
𝑥2 + 12.96 = 54.76
𝑥2 = 41.8
𝑥 = 6.47
hypotenuse
adjacent
opposite
𝑌𝑍
𝑋𝑌
𝑋𝑍
𝐻𝑈
𝑈𝐼
𝐻𝐼
trigonometric ratio
SOH CAH TOA
lengthright acute
SOH CAH TOA
𝑂𝑃𝑃
𝐴𝐷𝐽=
20
15=
4
3
𝑂𝑃𝑃
𝐴𝐷𝐽=
16
30=
8
15
𝑂𝑃𝑃
𝐴𝐷𝐽=
14
48=
7
24
𝑂𝑃𝑃
𝐻𝑌𝑃=
15
25=
3
5
𝑂𝑃𝑃
𝐻𝑌𝑃=
30
34=
15
17
𝐴𝐷𝐽
𝐻𝑌𝑃=
48
50=
24
25
=11
29=
11
29=
25
29
=25
11=
18
7= 1
UNIT 3: RIGHT TRIANGLE TRIGONOMETRY
3.2 Finding Sides and Angles
of Right Triangles
function
inputangle
output
x
sin 19° =𝑥
11
11 ∙ sin 19° = 𝑥
3.58 = 𝑥
x
cos 46° =19.2
𝑥
𝑥 =19.2
cos 46°
𝑥 = 27.64
sin 𝑅 =𝑂𝑃𝑃
𝐻𝑌𝑃 cos 𝐶 =𝐴𝐷𝐽
𝐻𝑌𝑃
x
sin 34° =11
𝑥
𝑥 =11
sin 34°
𝑥 = 19.67
sin 𝐻 =𝑂𝑃𝑃
𝐻𝑌𝑃
14.63 = 𝑥
x
𝑥 = 15.49
tan 26° =𝑂𝑃𝑃
𝐴𝐷𝐽tan 50° =
𝐴𝐷𝐽
𝐻𝑌𝑃
𝑥 = 6.92
tan 20° =𝑂𝑃𝑃
𝐴𝐷𝐽
sin-1 cos-1 tan-1
tan−1 𝑥 = 1
tan−1 1 = 𝑥
45° = 𝑥
tan−1 𝑥 =5
5
tan−15
12= 𝑥
22.6° = 𝑥
tan−1 𝑥 =5
12
cos−120
21= 𝑥
17.8° = 𝑥
cos−1 𝑥 =40
42
cos−115
28= 𝑥
57.6° = 𝑥
sin−119
23= 𝑥
55.7° = 𝑥cos−1
35
43= 𝑥
35.5° = 𝑥
UNIT 3: RIGHT TRIANGLE TRIGONOMETRY
3.3 Sine and Cosine of
Complementary Angles
•G.SRT.7 Explain and use
the relationship between the sine and cosine of complementary angles
What am I learning today?
•Find the complement of sine and cosine
What am I going to do today?
•5 Question Daily Assessment
•Daily Ticket out the Door
How will I show you that I’ve learned it?
180˚
90˚
complementary
Opposite angle
cosine
•G.SRT.7 Explain and use
the relationship between the sine and cosine of complementary angles
What am I learning today?
•Find the complement of sine and cosine
What am I going to do today?
•5 Question Daily Assessment
•Daily Ticket out the Door
How will I show you that I’ve learned it?
= 𝐜𝐨𝐬 𝟐𝟔° = 𝐬𝐢𝐧 𝟔° = 𝐬𝐢𝐧 𝟓𝟐°
= 𝐜𝐨𝐬 𝟔𝟔° = 𝐬𝐢𝐧 𝟏𝟖° = 𝐜𝐨𝐬 𝟒𝟓°
= 𝐜𝐨𝐬 𝟔𝟖° = 𝐬𝐢𝐧 𝟐𝟓° = 𝐬𝐢𝐧 𝟒𝟔°
= 𝐜𝐨𝐬 𝟓𝟖° = 𝐬𝐢𝐧 𝟔𝟓° = 𝐜𝐨𝐬 𝟕𝟓°
•G.SRT.7 Explain and use
the relationship between the sine and cosine of complementary angles
What am I learning today?
•Find the complement of sine and cosine
What am I going to do today?
•5 Question Daily Assessment
•Daily Ticket out the Door
How will I show you that I’ve learned it?
𝟒
𝟓
𝟒
𝟓
𝟑
𝟓
𝟑
𝟓
Sin A and Cos B are the same which means The complement of sine and cosine are equal.
•G.SRT.7 Explain and use
the relationship between the sine and cosine of complementary angles
What am I learning today?
•Find the complement of sine and cosine
What am I going to do today?
•5 Question Daily Assessment
•Daily Ticket out the Door
How will I show you that I’ve learned it?
𝟎. 𝟓
𝟎. 𝟓𝟎. 𝟖𝟔𝟔
𝟎. 𝟖𝟔𝟔
Then mQ = 60˚
The complement of sine and cosine are equal.
•G.SRT.7 Explain and use
the relationship between the sine and cosine of complementary angles
What am I learning today?
•Find the complement of sine and cosine
What am I going to do today?
•5 Question Daily Assessment
•Daily Ticket out the Door
How will I show you that I’ve learned it?
102 + 242 = 𝑥2
100 + 576 = 𝑥2
676 = 𝑥2
26 = 𝑥
26
𝟐𝟒
𝟐𝟔
𝟏𝟎
𝟐𝟔=
𝟓
𝟏𝟑
The complement of sine and cosine are equal.
=𝟏𝟐
𝟏𝟑
𝟐𝟒
𝟐𝟔=
𝟏𝟐
𝟏𝟑
𝟏𝟎
𝟐𝟔=
𝟓
𝟏𝟑 𝟎. 𝟕𝟎𝟕 𝟎. 𝟕𝟎𝟕
𝟎. 𝟕𝟎𝟕 𝟎. 𝟕𝟎𝟕
Then mT = 45˚
•G.SRT.7 Explain and use
the relationship between the sine and cosine of complementary angles
What am I learning today?
•Find the complement of sine and cosine
What am I going to do today?
•5 Question Daily Assessment
•Daily Ticket out the Door
How will I show you that I’ve learned it?
𝐜𝐨𝐬 𝟓𝟐° ≈ 𝟎. 𝟔𝟏𝟔
𝐬𝐢𝐧 𝟑𝟎° ≈ 𝟎. 𝟓
•G.SRT.7 Explain and use
the relationship between the sine and cosine of complementary angles
What am I learning today?
•Find the complement of sine and cosine
What am I going to do today?
•5 Question Daily Assessment
•Daily Ticket out the Door
How will I show you that I’ve learned it?
5
C B
A
12
35
H T
A
12
52 + 122 = 𝑥2
25 + 144 = 𝑥2
169 = 𝑥2
13 = 𝑥
13
13
𝟓
𝟏𝟑𝟓
𝟏𝟑
122 + 352 = 𝑥2
144 + 1225 = 𝑥2
1369 = 𝑥2
37 = 𝑥
37
37𝟏𝟐
𝟑𝟕𝟏𝟐
𝟑𝟕
•G.SRT.7 Explain and use
the relationship between the sine and cosine of complementary angles
What am I learning today?
•Find the complement of sine and cosine
What am I going to do today?
•5 Question Daily Assessment
•Daily Ticket out the Door
How will I show you that I’ve learned it?
8
Y Z
X
6
82 + 62 = 𝑥2
64 + 36 = 𝑥2
100 = 𝑥2
10 = 𝑥
10
10
𝟒
𝟓𝟒
𝟓
3
I M
X
4
32 + 𝑥2 = 52
9 + 𝑥2 = 25
𝑥2 = 16
𝑥 = 4
10
5
𝟒
𝟓𝟒
𝟓
•G.SRT.7 Explain and use
the relationship between the sine and cosine of complementary angles
What am I learning today?
•Find the complement of sine and cosine
What am I going to do today?
•5 Question Daily Assessment
•Daily Ticket out the Door
How will I show you that I’ve learned it?
•G.SRT.7 Explain and use
the relationship between the sine and cosine of complementary angles
What am I learning today?
•Find the complement of sine and cosine
What am I going to do today?
•5 Question Daily Assessment
•Daily Ticket out the Door
How will I show you that I’ve learned it?
UNIT 3: RIGHT TRIANGLE TRIGONOMETRY3.4 Solve Right Triangles
•G.SRT.8 Use trigonometric
ratios and the Pythagorean Theorem to solve triangles in applied problems
What am I learning today?
•Use the Pythagorean Theorem to Solve Right Triangles
•Use Trigonometric Ratios to Solve Right Triangles
What am I going to do today?
• 5 Question Daily Assessment
•Daily Ticket out the Door
How will I show you that I’ve learned it?
solve
Side lengths
angle
The length of two sides
The length of 1 side and 1 acute angle
The length of 1 side and 1 trigonometric ratio
•G.SRT.8 Use trigonometric
ratios and the Pythagorean Theorem to solve triangles in applied problems
What am I learning today?
•Use the Pythagorean Theorem to Solve Right Triangles
•Use Trigonometric Ratios to Solve Right Triangles
What am I going to do today?
• 5 Question Daily Assessment
•Daily Ticket out the Door
How will I show you that I’ve learned it?
3.12 + 8.92 = 𝑥2
9.61 + 79.21 = 𝑥2
88.82 = 𝑥2
9.4 = 𝑥9.4
19.2˚
70.8˚
9.4tan−1
3.1
8.9= ∠𝑃
19.2° = ∠𝑃
R = 90 – 19.2 = 70.8˚
•G.SRT.8 Use trigonometric
ratios and the Pythagorean Theorem to solve triangles in applied problems
What am I learning today?
•Use the Pythagorean Theorem to Solve Right Triangles
•Use Trigonometric Ratios to Solve Right Triangles
What am I going to do today?
• 5 Question Daily Assessment
•Daily Ticket out the Door
How will I show you that I’ve learned it?
𝑥2 + 3.92 = 7.42
𝑥2 + 15.21 = 54.76𝑥2 = 39.55
𝑥 = 6.3
3.9
6.3˚
58˚
3.9
C = 90 – 32 = 58˚
sin 32° =𝐵𝐶
7.4
3.58 = 𝑥
6.3
•G.SRT.8 Use trigonometric
ratios and the Pythagorean Theorem to solve triangles in applied problems
What am I learning today?
•Use the Pythagorean Theorem to Solve Right Triangles
•Use Trigonometric Ratios to Solve Right Triangles
What am I going to do today?
• 5 Question Daily Assessment
•Daily Ticket out the Door
How will I show you that I’ve learned it?
Angle of Elevation
Angle of Depression
•G.SRT.8 Use trigonometric
ratios and the Pythagorean Theorem to solve triangles in applied problems
What am I learning today?
•Use the Pythagorean Theorem to Solve Right Triangles
•Use Trigonometric Ratios to Solve Right Triangles
What am I going to do today?
• 5 Question Daily Assessment
•Daily Ticket out the Door
How will I show you that I’ve learned it?
•G.SRT.8 Use trigonometric
ratios and the Pythagorean Theorem to solve triangles in applied problems
What am I learning today?
•Use the Pythagorean Theorem to Solve Right Triangles
•Use Trigonometric Ratios to Solve Right Triangles
What am I going to do today?
• 5 Question Daily Assessment
•Daily Ticket out the Door
How will I show you that I’ve learned it?
•G.SRT.8 Use trigonometric
ratios and the Pythagorean Theorem to solve triangles in applied problems
What am I learning today?
•Use the Pythagorean Theorem to Solve Right Triangles
•Use Trigonometric Ratios to Solve Right Triangles
What am I going to do today?
• 5 Question Daily Assessment
•Daily Ticket out the Door
How will I show you that I’ve learned it?
618.75 ft2
•G.SRT.8 Use trigonometric
ratios and the Pythagorean Theorem to solve triangles in applied problems
What am I learning today?
•Use the Pythagorean Theorem to Solve Right Triangles
•Use Trigonometric Ratios to Solve Right Triangles
What am I going to do today?
• 5 Question Daily Assessment
•Daily Ticket out the Door
How will I show you that I’ve learned it?
991.86 ft2
•G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems
What am I learning today?
•Use the Pythagorean Theorem to Solve Right Triangles
•Use Trigonometric Ratios to Solve Right Triangles
What am I going to do today?
• 5 Question Daily Assessment
•Daily Ticket out the Door
How will I show you that I’ve learned it?
•G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems
What am I learning today?
•Use the Pythagorean Theorem to Solve Right Triangles
•Use Trigonometric Ratios to Solve Right Triangles
What am I going to do today?
• 5 Question Daily Assessment
•Daily Ticket out the Door
How will I show you that I’ve learned it?
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