Key content

The Pythagorean Theorem or Pythagoras’ theorem, was given by Pythagoras of Samos, who was an ancient Ionian Greek Philosopher. Pythagoras’ Theorem is a Mathematical relation between the sides of a right-angled Triangle.

Right Angled Triangle: A right angle Triangle or right-angled triangle is a triangle that has one angle is a right angle or a 90° angle.  The side opposite to the angle is called the hypotenuse, and the sides adjacent to the right angle are called the base and height.

This is a right-angled triangle, and from the figure, we can see that the side opposite to the right angle is the hypotenuse.

A right-angled triangle is the basis of all trigonometric operations.

Formula:

(Hypotenuse)2  =(Base) 2+ (Height)2

For Example, a right-angle triangle with a height of 4cm and a base of 3 cm, find the hypotenuse of the triangle.

So we a triangle with base = 3 cm and height=4cm,

                    Therefore, using Pythagoras’ theorem

                     (Hypotenuse)2  =(Base) 2+ (Height)2

                      (Hypotenuse)2  =(3) 2+ (4)2

                      (Hypotenuse)2  = 9 + 16

                      (Hypotenuse)2  =25

                         Hypotenuse = 5

  Examples

🔹 Example 1: Find the Hypotenuse

Given:

  • a=3
  • b=4

                c2=(3)2+(4)2

                c2 =9+16

                 c2=25

                  c​=5

Answer: c=5

🔹 Example 2: Find a Missing Leg

Given:

  • c=13
  • b=5

a2=c2−b2

a2=(13)2−(5)2

a2=169−25

a2=144

a​=12

Answer: a=12             

For more such learnings, you can visit TutorBin.

Real-Life Applications

1. Construction & Architecture

Builders use the Pythagorean theorem to ensure walls are square and rooms are correctly proportioned. For instance, measuring 3 feet along one wall and 4 feet along another, the diagonal between them should be 5 feet for a perfect right angle.

 2. Navigation & Mapping

To calculate the shortest distance between two points (e.g., a direct line across a field or body of water), the theorem helps find the straight-line distance (hypotenuse) from two perpendicular paths.

3. Aviation

Pilots use it for calculating direct flight paths, determining how far they’ve flown north and east to calculate their actual straight-line distance from the starting point.

 4. Computer Graphics

Used in rendering 3D objects and calculating distances between pixels on the screen.

 5. Surveying

Surveyors apply it to determine distances and property boundaries.

FREQUENTLY ASKED QUESTIONS

1. What is Pythagoras’ Theorem?

Pythagoras’ Theorem is a relationship between the sides of a right-angle triangle. The formula for the Pythagorean theorem
(Hypotenuse)2  =(Base) 2+ (Height)2

2. How can we find the base of a right triangle if we have the hypotenuse and height of the Triangle?

To find the base of a triangle whose hypotenuse and base are known ,we can use the formula for the Pythagorean theorem in such a way.

For eg. we have a triangle with hypotenuse 7 and height 5, then the base of the triangle is given by:

(Base)2  =(Hypotenuse) 2– (Height)2

(Base)2  =(7) 2– (5)2

(Base)2  = 49 – 25

(Base)2  =24

Base =√24                                         

Base =4.8

3. What is the formula to determine the area of a right-angle triangle?

The Area of a right-angle triangle is given by:

Area=(Base * Height)/2

4. How can TutorBin help me with my studies?

TutoBin offers help in various ways, you can opt for homework help, video solutions, or live interactions with our Expert tutors. We offer help in various subjects and our experts are experienced individuals who work day and night to help students.

5. How can I register for online homework help from TutorBin?

 You can visit our website at https://tutorbin.com/, and you will find a sign-up option at the top right corner. As soon as you click on it you will be redirected to a page where you can fill in all your details, and then you can proceed with the homework, and you can opt for any kind of help.

Our Trending Services>> Homework Help | Assignment Help | Live Sessions | Do My Homework | Do My Essay | Write My Essay | Essay Writing Help | Lab Report Help | Project Report Help | Speech Writing Service | Presentation Writing Service | Video Solutions | Pay Someone To Do My Homework | Help With Writing My Paper | Writing Service For Research Paper | Paying Someone To Write Your Paper

Our Popular AI Tools>> AI Homework Helper | Essay Generator | Grammar Checker | Physics AI Solver | Chemistry AI Solver | Economics AI Solver | Math AI Solver |  Accounting AI Solver | Finance AI Solver | Biology AI Solver | Calculus AI Solver | Statistics AI Solver

New Websites >> Pay People to Do Your Homework | Pay for my Assignment | Write My Essays for Me | Help Accounting Homework | Economics Homework Help Online | Geometry Homework Help | Help Me Do My Essay | Help in Assignment

Stuck With Your Assignment? Get Your Assignment Done From Our Expert Writers $20 Reward Upon Registration
Place your order here
Please Wait ...
Spread the Love

Leave a Reply

Your email address will not be published.Required fields are marked*

comments

  1. Wow, fantastic weblog structure! How long have you ever been running a blog for? you made blogging look easy. The overall glance of your site is fantastic, let alone the content!

Online Homework Help

Get Homework Help

Get Answer within 15-30 minutes

x

Get Homework Help

×

Check out our free tool Math Problem Solver

About TutorBin

What do we do?

We offer an array of online homework help and other services for our students and tutors to choose from based on their needs and expertise. As an integrated platform for both tutors and students, we provide real time sessions, online assignment and homework help and project work assistance.

LEARN MORE
about tutorbin | what we do
about tutorbin | who we are

Who are we?

TutorBin is an integrated online homework help and tutoring platform serving as a one stop solution for students and online tutors. Students benefit from the experience and domain knowledge of global subject matter experts.

LEARN MORE
BACK TO TOP