Recent Lessons

Show all results for ""

Feature Overview

Ace your exams with our all-in-one platform for creating and sharing quizzes and tests.

Quizzes

Create quizzes and tests automatically from your content using AI.

Flashcards

Automatically turn your notes into digital flashcards.

Share, Export & Embed

Share with classmates or export to Excel and your learning management system.

Stats & Reporting

Auto-grading quizzes and tests with detailed stats and reports.

Mobile Apps

The smarter way to study – wherever you are.

Pricing

Search...

15 Questions

1 Views

Pythagorean Theorem and its Formulas

Choose a study mode

Play Quiz

Study Flashcards

Spaced Repetition

Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the formula for the Pythagorean Theorem?

c^2 = a^2 + b^2 (correct)

b = a^2 + c^2

a = c^2 + b^2

c = a^2 + b^2

In the Pythagorean Theorem formula, what does 'c' represent?

One of the two shorter sides

The sum of the squares of the two shorter sides

The result after subtracting a^2 from b^2

The length of the hypotenuse (correct)

Which formula is derived from the Pythagorean Theorem to find side 'a'?

a = c / b

a = sqrt(c^2 - b^2) (correct)

a = sqrt(c + b)

a = c - b

If a right triangle has sides 'a' and 'b', what would be the value of 'c' according to the Pythagorean Theorem?

sqrt(a^2 + b^2) Signup and view all the answers

Which operation is involved in calculating unknown side lengths using the Pythagorean Theorem formulas?

Square roots and addition Signup and view all the answers

What type of triangle has an interior angle of 90 degrees?

Right triangle Signup and view all the answers

Which side of a right triangle is opposite the right angle?

Hypotenuse Signup and view all the answers

How does the Pythagorean theorem relate the sides of a right triangle?

c^2 = a^2 + b^2 Signup and view all the answers

If a right triangle has sides of length 5 and 12, what is the length of the hypotenuse?

17 Signup and view all the answers

What is the significance of the Pythagorean theorem in solving right triangle problems?

It allows finding unknown side lengths in right triangles Signup and view all the answers

What is the Pythagorean theorem?

a^2 + b^2 = c^2 Signup and view all the answers

Who was the Greek mathematician who first recorded the Pythagorean theorem in writing?

Euclid Signup and view all the answers

In a right triangle with sides measuring 7 units and 24 units, what would be the length of the hypotenuse using the Pythagorean theorem?

25 Signup and view all the answers

Which field is NOT mentioned as an application of the Pythagorean theorem?

Astronomy Signup and view all the answers

What is the significance of understanding and applying the Pythagorean theorem?

It assists in solving problems involving right triangles Signup and view all the answers

Study Notes

The text discusses the Pythagorean Theorem, stating that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
The formula for the Pythagorean Theorem is: (c^2 = a^2 + b^2), where (c) is the hypotenuse and (a) and (b) are the other two sides.
Different formulas derived from the Pythagorean Theorem include: (a = \sqrt{c^2 - b^2}), (b = \sqrt{c^2 - a^2}), and (c = \sqrt{a^2 + b^2}).
Example exercises are given to apply the Pythagorean Theorem, such as finding the length of a side in a right triangle given the lengths of the other sides.
The exercises involve substituting the given values into the formulas derived from the Pythagorean Theorem to calculate the unknown side lengths, involving calculations like square roots and simplifying fractions.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

Explore the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. Learn about the formula c^2 = a^2 + b^2, along with derived formulas for finding side lengths. Practice applying the theorem with example exercises involving calculations like square roots and fractions.