Subjects

Geometry

Right Triangles & Trigonometry

Ratios in Right Triangles

Sine, Cosine, Tangent: Easy Trig Ratios for Right Triangles

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Sine, Cosine, Tangent: Easy Trig Ratios for Right Triangles

Ace E.

@acee._wujm

1 Follower

Understanding sine cosine tangent ratios in right triangles is essential for mastering trigonometry fundamentals. This comprehensive guide explains the three main trigonometric ratios and their practical applications in solving right triangle problems.

The sine ratio (sin θ) represents the relationship between the opposite side and hypotenuse
The cosine ratio (cos θ) compares the adjacent side to the hypotenuse
The tangent ratio (tan θ) relates the opposite side to the adjacent side
Solving trigonometry problems using soh cah toa involves identifying reference angles and applying appropriate ratios
Step-by-step problem-solving techniques demonstrate how to calculate angles in triangles using trigonometric ratios

10/6/2023

126

THE SINE RATIO
Ratio of the opposite side
(of the given angle other than in
90) to the hypoter use.
ex1
Wary 3
cometry
Unit 4-Right Triangle

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Applying Trigonometric Ratios

The second page demonstrates practical applications of trigonometric ratios through problem-solving examples. It outlines a systematic approach to solving for unknown sides in right triangles.

Highlight: A five-step problem-solving process:

Identify the reference angle
Label the three sides (Hypotenuse, Opposite, Adjacent)
Eliminate irrelevant sides
Select appropriate trigonometric function
Set up and solve the equation

Example: To solve for x using tan 41° = x/32:

Set up equation: x = 32(tan 41°)
Use calculator to compute
Round answer as specified (x ≈ 27.82)

Vocabulary: SOH CAH TOA is a mnemonic device for remembering trigonometric ratios:

SOH: Sine = Opposite/Hypotenuse
CAH: Cosine = Adjacent/Hypotenuse
TOA: Tangent = Opposite/Adjacent

View

Understanding Trigonometric Ratios

The first page introduces the three fundamental trigonometric ratios used in right triangle calculations. These ratios form the foundation for solving various trigonometric problems.

Definition: The sine ratio is the relationship between the opposite side of an angle (other than 90°) and the hypotenuse of a right triangle.

Definition: The cosine ratio compares the adjacent side of an angle (other than 90°) to the hypotenuse of a right triangle.

Definition: The tangent ratio represents the relationship between the opposite side and the adjacent side of an angle (other than 90°).

Vocabulary:

Opposite side: The side across from the reference angle
Adjacent side: The side next to the reference angle
Hypotenuse: The longest side of a right triangle, opposite to the right angle

Example: In a right triangle with sides 5, 12, and 13:

sin(A) = opposite/hypotenuse = 12/13
cos(A) = adjacent/hypotenuse = 5/13
tan(A) = opposite/adjacent = 12/5

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Knowunity is the # 1 ranked education app in five European countries

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Average App Rating

15 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

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iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying

Subjects

Geometry

Right Triangles & Trigonometry

Ratios in Right Triangles

Sine, Cosine, Tangent: Easy Trig Ratios for Right Triangles

Ace E.

@acee._wujm

1 Follower

The sine ratio (sin θ) represents the relationship between the opposite side and hypotenuse
The cosine ratio (cos θ) compares the adjacent side to the hypotenuse
The tangent ratio (tan θ) relates the opposite side to the adjacent side
Solving trigonometry problems using soh cah toa involves identifying reference angles and applying appropriate ratios
Step-by-step problem-solving techniques demonstrate how to calculate angles in triangles using trigonometric ratios

10/6/2023

126

9th

Geometry

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Applying Trigonometric Ratios

The second page demonstrates practical applications of trigonometric ratios through problem-solving examples. It outlines a systematic approach to solving for unknown sides in right triangles.

Highlight: A five-step problem-solving process:

Identify the reference angle
Label the three sides (Hypotenuse, Opposite, Adjacent)
Eliminate irrelevant sides
Select appropriate trigonometric function
Set up and solve the equation

Example: To solve for x using tan 41° = x/32:

Set up equation: x = 32(tan 41°)
Use calculator to compute
Round answer as specified (x ≈ 27.82)

Vocabulary: SOH CAH TOA is a mnemonic device for remembering trigonometric ratios:

SOH: Sine = Opposite/Hypotenuse
CAH: Cosine = Adjacent/Hypotenuse
TOA: Tangent = Opposite/Adjacent

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Understanding Trigonometric Ratios

The first page introduces the three fundamental trigonometric ratios used in right triangle calculations. These ratios form the foundation for solving various trigonometric problems.

Definition: The sine ratio is the relationship between the opposite side of an angle (other than 90°) and the hypotenuse of a right triangle.

Definition: The cosine ratio compares the adjacent side of an angle (other than 90°) to the hypotenuse of a right triangle.

Definition: The tangent ratio represents the relationship between the opposite side and the adjacent side of an angle (other than 90°).

Vocabulary:

Opposite side: The side across from the reference angle
Adjacent side: The side next to the reference angle
Hypotenuse: The longest side of a right triangle, opposite to the right angle

Example: In a right triangle with sides 5, 12, and 13:

sin(A) = opposite/hypotenuse = 12/13
cos(A) = adjacent/hypotenuse = 5/13
tan(A) = opposite/adjacent = 12/5

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Download in

Google Play

Download in

App Store

4.9+

Average App Rating

15 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Sine, Cosine, Tangent: Easy Trig Ratios for Right Triangles

Applying Trigonometric Ratios

Understanding Trigonometric Ratios

Similar Content

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

4.9+

15 M

#1

950 K+

Still not sure? Look at what your fellow peers are saying...

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

The application is very simple and well designed. So far I have found what I was looking for :D

Love this App ❤️, I use it basically all the time whenever I'm studying

Sine, Cosine, Tangent: Easy Trig Ratios for Right Triangles

Sign up to see the content. It's free!

Applying Trigonometric Ratios

Sign up to see the content. It's free!

Understanding Trigonometric Ratios

Similar Content

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

4.9+

15 M

#1

950 K+

Still not sure? Look at what your fellow peers are saying...

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

The application is very simple and well designed. So far I have found what I was looking for :D

Love this App ❤️, I use it basically all the time whenever I'm studying