T-1: Right Triangles and Trigonometric Ratios
Review:
Pythagorean Theorem: ___________________________
Review Practice: Find the missing side length of each right triangle.
a.)
b.)
Algebra 2: T-1 Right Triangles and Trigonometric Ratios
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The Parts of a Right Triangle
θ
θ
Hypotenuse:
Opposite:
Adjacent:
θ : Theta, pronounced ‘thay-tuh’
Three Trigonometric Ratios
Sine of θ: the ratio of the
_________________
Cosine of θ: the ratio of the
Tangent of θ: the ratio of the
“SOH CAH TOA” 
Example 1: Write trig equation relating each angle with the given side lengths.
a.)
1
b.)
c.)
2
2
30
3
60
1
Algebra 2: T-1 Right Triangles and Trigonometric Ratios
45
3
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Using Your Calculator
*Always make sure your calculator is in “Degree” mode.
Type sin 30 into your calculator. What is the answer?
Type cos 60 into your calculator. What is the answer?
Type tan 45 into your calculator. What is the answer?
Solving for a Missing Side
Example 2: Solve for x.
*To help you figure out which trigonometric ratio to use, label the sides opp, adj, or hyp.
a.)
x
b.)
c.)
x
8
20
x
55
7
Algebra 2: T-1 Right Triangles and Trigonometric Ratios
38
4
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Solving for a Missing Angle
Example 3: Solve for x.
*In order to solve for the angle, we have to use the Inverse function on our calculator. You need to
hit the “2nd” button before the trig ratio you want to use.
a.)
3
b.)
c.)
5
7
x
6
x
2
x
8
Three Other Trig Ratios
Cosecant of θ: the ratio of the ______
Secant of θ: the ratio of the
Cotangent of θ: the ratio of the
Algebra 2: T-1 Right Triangles and Trigonometric Ratios
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Example 4: Write trig equation relating each angle with the given side lengths.
a.)
1
b.)
c.)
2
2
30
3
60
1
45
3
Example 5: Find the rest of the trig ratios at angle A.
5
a) In ∆ABC, angle C is a right angle and sin 𝐴 = 13 .
3
b) In ∆ABC, angle C is a right angle and tan 𝐴 = .
4
Algebra 2: T-1 Right Triangles and Trigonometric Ratios
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15
c) In ∆ABC, angle C is a right angle and cos 𝐴 = 17 .
d) In ∆ABC, angle C is a right angle and sin 𝐴 =
7
25
.
Homework: p. 826 => 6 – 19a
Algebra 2: T-1 Right Triangles and Trigonometric Ratios
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