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Trigonometry Revision: SOH CAH TOA & Right Triangle Tricks for Kids with Photomath Tips

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Trigonometry Revision: SOH CAH TOA & Right Triangle Tricks for Kids with Photomath Tips

🌿𝑽𝒂𝒍🌿

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285 Followers

SOH CAH TOA: A Comprehensive Guide to Trigonometry in Right-Angled Triangles

This guide provides an in-depth explanation of trigonometry in right-angled triangles, focusing on the SOH CAH TOA mnemonic and its applications. It covers the basics of trigonometric ratios, methods for finding sides and angles, and practical examples using sine, cosine, and tangent functions.

Introduces the concept of trigonometry and its relevance to right-angled triangles
Explains the SOH CAH TOA formula and its components (Sine, Cosine, Tangent)
Demonstrates how to use trigonometric ratios to solve for unknown sides and angles
Provides step-by-step examples and calculations for various trigonometric problems
Includes visual aids and diagrams to enhance understanding of concepts

16/05/2023

625

Trigonometry Introduction
Trigonometry is another
branch of maths which is all
about finding the angles and
sides of commonly a right-
angle

Cosine Ratio and Its Applications

This page introduces the cosine ratio and demonstrates its use in finding unknown sides and angles in right-angled triangles. The cosine ratio is defined as the adjacent side divided by the hypotenuse.

Formula: Cosine = Adjacent / Hypotenuse

Two examples are provided to illustrate the application of the cosine ratio:

Example 1: Finding the adjacent side when given the hypotenuse and angle:

In a triangle with a 40° angle and a hypotenuse of 6 cm: cos 40° = x / 6 x = 6 × cos 40° x ≈ 2.05 cm (rounded to 2 decimal places)

Example 2: Finding the adjacent side when given the hypotenuse and angle:

In a triangle with a 45° angle and a hypotenuse of 3 m: cos 45° = x / 3 x = 3 × cos 45° x ≈ 0.92 cm (rounded to 2 decimal places)

View

Finding Angles Using the Tangent Ratio

This page focuses on using the tangent ratio to find unknown angles in right-angled triangles. It provides two examples to demonstrate different scenarios.

Example 1: Finding an unknown angle when given the opposite and adjacent sides:

In a triangle with an opposite side of 2.8 cm and an adjacent side of 4.66 cm: tan x = 2.8 / 4.66 x = tan⁻¹(2.8 / 4.66) x ≈ 31° (rounded to the nearest degree)

Example 2: Finding an unknown angle when given the opposite and adjacent sides:

In a triangle with an opposite side of 2 cm and an adjacent side of 7 cm: tan x = 2 / 7 x = tan⁻¹(2 / 7) x ≈ 26.57° (rounded to 2 decimal places)

Highlight: When finding an angle using the tangent ratio, use the inverse tangent function (tan⁻¹ or arctan) on your calculator.

View

Tangent Ratio and Its Applications

This page introduces the tangent ratio and demonstrates its use in finding unknown sides in right-angled triangles. The tangent ratio is defined as the opposite side divided by the adjacent side.

Formula: Tangent = Opposite / Adjacent

An example is provided to illustrate the application of the tangent ratio:

Example: Finding the opposite side when given the adjacent side and angle:

In a triangle with a 22° angle and an adjacent side of 18 cm: tan 22° = x / 18 x = 18 × tan 22° x ≈ 7.27 cm (rounded to 2 decimal places)

This example shows how to use the tangent ratio to find an unknown side length.

View

Finding Angles Using the Sine Ratio

This page explains how to use the sine ratio to find unknown angles in a right-angled triangle. It provides two examples to illustrate different scenarios.

Example 1: Finding the opposite side when given the hypotenuse and angle:

In a triangle with a 60° angle and a hypotenuse of 50 cm: sin 60° = x / 50 x = 50 × sin 60° x ≈ 43.30 cm (rounded to 2 decimal places)

Example 2: Finding an unknown angle when given the opposite and hypotenuse:

In a triangle with an opposite side of 7.4 cm and a hypotenuse of 9 cm: sin x = 7.4 / 9 x = sin⁻¹(7.4 / 9) x ≈ 55.31° (rounded to 2 decimal places)

Highlight: When finding an angle, use the inverse sine function (sin⁻¹ or arcsin) on your calculator.

View

Introduction to Trigonometry

This page introduces the fundamental concepts of trigonometry, focusing on its application to right-angled triangles. Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. In right-angled triangles, the sides are given specific names based on their position relative to the angle being considered.

Definition: Trigonometry is the study of relationships between the sides and angles of triangles, particularly right-angled triangles.

The three sides of a right-angled triangle are defined as follows:

Hypotenuse: The longest side of the triangle, opposite the right angle.
Adjacent: The side next to the angle being considered, connecting it to the hypotenuse.
Opposite: The remaining side of the triangle, across from the angle being considered.

Highlight: Understanding the naming convention of triangle sides is crucial for applying trigonometric ratios correctly.

View

Trigonometric Ratios and SOH CAH TOA

This page delves deeper into the concept of trigonometric ratios and introduces the SOH CAH TOA mnemonic. It explains how the placement of the angle can affect the labeling of sides and emphasizes the importance of correctly identifying the opposite, adjacent, and hypotenuse sides.

Vocabulary: SOH CAH TOA is a mnemonic device used to remember the three main trigonometric ratios: Sine, Cosine, and Tangent.

The SOH CAH TOA formula breaks down as follows:

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

Highlight: The placement of the angle can change which side is considered opposite or adjacent, but the hypotenuse always remains the longest side opposite the right angle.

View

Conclusion and Practice

This final page would typically include a summary of the key concepts covered in the guide and provide suggestions for further practice. However, as this page is not explicitly described in the given transcript, we can infer that it might contain the following elements:

A recap of the SOH CAH TOA formula and its importance in solving right-angled triangle problems
Encouragement to practice using all three trigonometric ratios (sine, cosine, and tangent) for both finding sides and angles
Suggestions for additional resources, such as SOH CAH TOA worksheets or online SOHCAHTOA calculators
Reminders about the importance of proper angle placement and side identification in right-angled triangles
Tips for choosing the appropriate trigonometric ratio based on the given information in a problem

Highlight: Regular practice with a variety of problems is key to mastering trigonometry and becoming proficient in using the SOH CAH TOA technique.

View

Sine Ratio and Its Applications

This page focuses on the sine ratio and demonstrates how to use it for finding unknown sides in a right-angled triangle. The sine ratio is defined as the opposite side divided by the hypotenuse.

Formula: Sine = Opposite / Hypotenuse

An example is provided to illustrate the use of the sine ratio:

Example: In a right-angled triangle with a 40° angle and an opposite side of 8 cm, the hypotenuse can be calculated using the sine rule:

sin 40° = 8 / x x = 8 / sin 40° x ≈ 12.45 cm (rounded to 2 decimal places)

This example demonstrates how to solve for an unknown side using the sine ratio and a calculator.

View

Finding Angles Using the Cosine Ratio

This page focuses on using the cosine ratio to find unknown angles in right-angled triangles. It provides an example to demonstrate the process.

Example: Finding an unknown angle when given the adjacent side and hypotenuse:

In a triangle with an adjacent side of 7 cm and a hypotenuse of 20 cm: cos x = 7 / 20 x = cos⁻¹(7 / 20) x ≈ 69.51° (rounded to 2 decimal places)

Highlight: When finding an angle using the cosine ratio, use the inverse cosine function (cos⁻¹ or arccos) on your calculator.

View

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Subjects

Maths

Geometry & measures

Angles

Trigonometry Revision: SOH CAH TOA & Right Triangle Tricks for Kids with Photomath Tips

🌿𝑽𝒂𝒍🌿

@xx_val_xx

285 Followers

SOH CAH TOA: A Comprehensive Guide to Trigonometry in Right-Angled Triangles

Introduces the concept of trigonometry and its relevance to right-angled triangles
Explains the SOH CAH TOA formula and its components (Sine, Cosine, Tangent)
Demonstrates how to use trigonometric ratios to solve for unknown sides and angles
Provides step-by-step examples and calculations for various trigonometric problems
Includes visual aids and diagrams to enhance understanding of concepts

16/05/2023

625

11/9

Maths

Cosine Ratio and Its Applications

Formula: Cosine = Adjacent / Hypotenuse

Two examples are provided to illustrate the application of the cosine ratio:

Example 1: Finding the adjacent side when given the hypotenuse and angle:

In a triangle with a 40° angle and a hypotenuse of 6 cm: cos 40° = x / 6 x = 6 × cos 40° x ≈ 2.05 cm (rounded to 2 decimal places)

Example 2: Finding the adjacent side when given the hypotenuse and angle:

In a triangle with a 45° angle and a hypotenuse of 3 m: cos 45° = x / 3 x = 3 × cos 45° x ≈ 0.92 cm (rounded to 2 decimal places)

Finding Angles Using the Tangent Ratio

This page focuses on using the tangent ratio to find unknown angles in right-angled triangles. It provides two examples to demonstrate different scenarios.

Example 1: Finding an unknown angle when given the opposite and adjacent sides:

In a triangle with an opposite side of 2.8 cm and an adjacent side of 4.66 cm: tan x = 2.8 / 4.66 x = tan⁻¹(2.8 / 4.66) x ≈ 31° (rounded to the nearest degree)

Example 2: Finding an unknown angle when given the opposite and adjacent sides:

In a triangle with an opposite side of 2 cm and an adjacent side of 7 cm: tan x = 2 / 7 x = tan⁻¹(2 / 7) x ≈ 26.57° (rounded to 2 decimal places)

Highlight: When finding an angle using the tangent ratio, use the inverse tangent function (tan⁻¹ or arctan) on your calculator.

Tangent Ratio and Its Applications

This page introduces the tangent ratio and demonstrates its use in finding unknown sides in right-angled triangles. The tangent ratio is defined as the opposite side divided by the adjacent side.

Formula: Tangent = Opposite / Adjacent

An example is provided to illustrate the application of the tangent ratio:

Example: Finding the opposite side when given the adjacent side and angle:

In a triangle with a 22° angle and an adjacent side of 18 cm: tan 22° = x / 18 x = 18 × tan 22° x ≈ 7.27 cm (rounded to 2 decimal places)

This example shows how to use the tangent ratio to find an unknown side length.

Finding Angles Using the Sine Ratio

This page explains how to use the sine ratio to find unknown angles in a right-angled triangle. It provides two examples to illustrate different scenarios.

Example 1: Finding the opposite side when given the hypotenuse and angle:

In a triangle with a 60° angle and a hypotenuse of 50 cm: sin 60° = x / 50 x = 50 × sin 60° x ≈ 43.30 cm (rounded to 2 decimal places)

Example 2: Finding an unknown angle when given the opposite and hypotenuse:

In a triangle with an opposite side of 7.4 cm and a hypotenuse of 9 cm: sin x = 7.4 / 9 x = sin⁻¹(7.4 / 9) x ≈ 55.31° (rounded to 2 decimal places)

Highlight: When finding an angle, use the inverse sine function (sin⁻¹ or arcsin) on your calculator.

Introduction to Trigonometry

Definition: Trigonometry is the study of relationships between the sides and angles of triangles, particularly right-angled triangles.

The three sides of a right-angled triangle are defined as follows:

Hypotenuse: The longest side of the triangle, opposite the right angle.
Adjacent: The side next to the angle being considered, connecting it to the hypotenuse.
Opposite: The remaining side of the triangle, across from the angle being considered.

Highlight: Understanding the naming convention of triangle sides is crucial for applying trigonometric ratios correctly.

Trigonometric Ratios and SOH CAH TOA

Vocabulary: SOH CAH TOA is a mnemonic device used to remember the three main trigonometric ratios: Sine, Cosine, and Tangent.

The SOH CAH TOA formula breaks down as follows:

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

Highlight: The placement of the angle can change which side is considered opposite or adjacent, but the hypotenuse always remains the longest side opposite the right angle.

Conclusion and Practice

A recap of the SOH CAH TOA formula and its importance in solving right-angled triangle problems
Encouragement to practice using all three trigonometric ratios (sine, cosine, and tangent) for both finding sides and angles
Suggestions for additional resources, such as SOH CAH TOA worksheets or online SOHCAHTOA calculators
Reminders about the importance of proper angle placement and side identification in right-angled triangles
Tips for choosing the appropriate trigonometric ratio based on the given information in a problem

Highlight: Regular practice with a variety of problems is key to mastering trigonometry and becoming proficient in using the SOH CAH TOA technique.

Sine Ratio and Its Applications

This page focuses on the sine ratio and demonstrates how to use it for finding unknown sides in a right-angled triangle. The sine ratio is defined as the opposite side divided by the hypotenuse.

Formula: Sine = Opposite / Hypotenuse

An example is provided to illustrate the use of the sine ratio:

Example: In a right-angled triangle with a 40° angle and an opposite side of 8 cm, the hypotenuse can be calculated using the sine rule:

sin 40° = 8 / x x = 8 / sin 40° x ≈ 12.45 cm (rounded to 2 decimal places)

This example demonstrates how to solve for an unknown side using the sine ratio and a calculator.

Finding Angles Using the Cosine Ratio

This page focuses on using the cosine ratio to find unknown angles in right-angled triangles. It provides an example to demonstrate the process.

Example: Finding an unknown angle when given the adjacent side and hypotenuse:

In a triangle with an adjacent side of 7 cm and a hypotenuse of 20 cm: cos x = 7 / 20 x = cos⁻¹(7 / 20) x ≈ 69.51° (rounded to 2 decimal places)