Subjects

Physics

Energy and fields

Let's Learn: Solving Right Triangles and Understanding Vectors

Name: Knowunity
Brand: Knowunity

View

Let's Learn: Solving Right Triangles and Understanding Vectors

Jessica Lindeman

@jessicalindeman_cszz

22 Followers

Solving right triangles using Pythagorean theorem and Understanding vector components in physics form the foundation of this comprehensive math review for vectors in Physics 421.

• The document covers essential mathematical concepts including the Pythagorean theorem, trigonometric ratios, and vector analysis
• Detailed explanations of vector components, resolution, and addition are provided with practical examples
• Special emphasis is placed on trigonometric values in triangle labeling and solving real-world physics problems
• The material progresses from basic right triangle calculations to complex vector addition scenarios

2/12/2023

189

View

Page 1: Pythagorean Theorem Review

This page introduces the fundamental relationship between sides of a right triangle using the Pythagorean theorem. The content focuses on practical problem-solving using the formula a² + b² = c².

Definition: The Pythagorean theorem states that in a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides.

Example: A right triangle with sides 8 and 6 units has its hypotenuse calculated as √(64 + 36) = 10 units.

Highlight: The formula a² + b² = c² is essential for solving unknown sides in right triangles.

View

Page 2: Trigonometric Ratios

The second page explores basic trigonometric ratios and their applications in right triangles, introducing sine, cosine, and tangent relationships.

Vocabulary:

Sine (sin θ) = opposite/hypotenuse
Cosine (cos θ) = adjacent/hypotenuse
Tangent (tan θ) = opposite/adjacent

Example: In a right triangle with sides 3, 4, and 5 units, sin C = 3/5, cos C = 4/5, and tan C = 3/4.

View

Page 7: Vector Addition Methods

This page outlines the systematic approach to vector addition problems.

Definition: Four key steps for solving vector addition problems are presented:

Sketch and resolve vectors
Add x and y components
Draw component triangle
Calculate resultant magnitude and direction

Example: Addition of vectors including 20 N along positive x-axis and another at 30° above.

View

Page 4: Vector Components

Detailed explanation of vector component calculations using trigonometric functions, with practical applications.

Example: A plane flying at 123 km/h at 40° above the x-axis has components:

X-component = 123 cos(40°) = 94.2 km/h
Y-component = 123 sin(40°) = 79.1 km/h

Highlight: Component calculations rely on cosine for x-components and sine for y-components.

View

Page 3: Introduction to Vectors

This page introduces vector concepts and their fundamental properties in physics, including definition and representation methods.

Definition: A vector is a quantity that has both magnitude and direction.

Highlight: Vector components can be broken down into x and y components parallel to the coordinate axes.

Example: Angles can be measured either counterclockwise from the positive x-axis or as degrees above/below the x-axis.

View

Page 7: Advanced Vector Addition

Comprehensive coverage of vector addition problem-solving methodology with multiple examples.

Highlight: Four key steps for vector addition:

Sketch and resolve each vector
Add x and y components
Draw resultant triangle
Calculate magnitude and direction

Example: Adding vectors of 4.0m 90° below x-axis and 8.3m 55° above negative x-axis results in 5.6m at 30.3° above negative x-axis.

View

Page 6: Vector Addition

Introduction to vector addition methods and resultant vector calculations.

Definition: The resultant vector is the single vector that has the same effect as two or more vectors acting together.

Example: Adding 20 N East and 7 N North vectors results in a 21.2 N resultant at 19.3° above the positive x-axis.

View

Page 5: Vector Component Practice

This page provides practice problems for calculating vector components with negative angles and forces.

Example: For 18 km at 47° below the positive x-axis:

X-component = 18 cos(47°) = 12.3 km
Y-component = 18 sin(47°) = -13.1 km

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

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

4.9+

Average App Rating

13 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

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

Subjects

Physics

Energy and fields

Let's Learn: Solving Right Triangles and Understanding Vectors

Jessica Lindeman

@jessicalindeman_cszz

22 Followers

Solving right triangles using Pythagorean theorem and Understanding vector components in physics form the foundation of this comprehensive math review for vectors in Physics 421.

2/12/2023

189

Physics

Page 1: Pythagorean Theorem Review

This page introduces the fundamental relationship between sides of a right triangle using the Pythagorean theorem. The content focuses on practical problem-solving using the formula a² + b² = c².

Definition: The Pythagorean theorem states that in a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides.

Example: A right triangle with sides 8 and 6 units has its hypotenuse calculated as √(64 + 36) = 10 units.

Highlight: The formula a² + b² = c² is essential for solving unknown sides in right triangles.

Page 2: Trigonometric Ratios

The second page explores basic trigonometric ratios and their applications in right triangles, introducing sine, cosine, and tangent relationships.

Vocabulary:

Sine (sin θ) = opposite/hypotenuse
Cosine (cos θ) = adjacent/hypotenuse
Tangent (tan θ) = opposite/adjacent

Example: In a right triangle with sides 3, 4, and 5 units, sin C = 3/5, cos C = 4/5, and tan C = 3/4.

Page 7: Vector Addition Methods

This page outlines the systematic approach to vector addition problems.

Definition: Four key steps for solving vector addition problems are presented:

Sketch and resolve vectors
Add x and y components
Draw component triangle
Calculate resultant magnitude and direction

Example: Addition of vectors including 20 N along positive x-axis and another at 30° above.

Page 4: Vector Components

Detailed explanation of vector component calculations using trigonometric functions, with practical applications.

Example: A plane flying at 123 km/h at 40° above the x-axis has components:

X-component = 123 cos(40°) = 94.2 km/h
Y-component = 123 sin(40°) = 79.1 km/h

Highlight: Component calculations rely on cosine for x-components and sine for y-components.

Page 3: Introduction to Vectors

This page introduces vector concepts and their fundamental properties in physics, including definition and representation methods.

Definition: A vector is a quantity that has both magnitude and direction.

Highlight: Vector components can be broken down into x and y components parallel to the coordinate axes.

Example: Angles can be measured either counterclockwise from the positive x-axis or as degrees above/below the x-axis.

Page 7: Advanced Vector Addition

Comprehensive coverage of vector addition problem-solving methodology with multiple examples.

Highlight: Four key steps for vector addition:

Sketch and resolve each vector
Add x and y components
Draw resultant triangle
Calculate magnitude and direction

Example: Adding vectors of 4.0m 90° below x-axis and 8.3m 55° above negative x-axis results in 5.6m at 30.3° above negative x-axis.

Page 6: Vector Addition

Introduction to vector addition methods and resultant vector calculations.

Definition: The resultant vector is the single vector that has the same effect as two or more vectors acting together.

Example: Adding 20 N East and 7 N North vectors results in a 21.2 N resultant at 19.3° above the positive x-axis.

Page 5: Vector Component Practice

This page provides practice problems for calculating vector components with negative angles and forces.

Example: For 18 km at 47° below the positive x-axis:

X-component = 18 cos(47°) = 12.3 km
Y-component = 18 sin(47°) = -13.1 km

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

13 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