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# Pythagorean Theorem

The Pythagorean Theorem is a fundamental concept in mathematics that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

• Pythagorean Theorem
• Solved Examples
• FAQs

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## Pythagorean Theorem

In mathematical notation, the theorem can be written as:

c^2 = a^2 + b^2

where c is the length of the hypotenuse, and a and b are the lengths of the other two sides of the right triangle. The Pythagorean Theorem is named after the ancient Greek mathematician Pythagoras, who is credited with discovering the theorem. The theorem has many practical applications in fields such as architecture, engineering, and physics, and is an important tool in many areas of mathematics.

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## Solved examples

Example 1:
Find the length of the hypotenuse of a right triangle with legs of length 3 and 4.

Solution:
Using the Pythagorean Theorem, we have:

c^2 = a^2 + b^2
c^2 = 3^2 + 4^2
c^2 = 9 + 16
c^2 = 25
c = 5

Therefore, the length of the hypotenuse is 5 units.

Example 2:
A ladder is leaning against a wall. The bottom of the ladder is 6 feet away from the wall, and the ladder is 8 feet long. What is the height at which ladder touches the wall?

Solution:
We can model this situation as a right triangle, with the ladder as the hypotenuse, the distance from the wall as one leg, and the height at which ladder touches the wall as the other leg. Using the Pythagorean Theorem, we have:

c^2 = a^2 + b^2
8^2 = 6^2 + b^2
64 = 36 + b^2
b^2 = 28
b = sqrt(28)

Therefore, the height of the ladder above the ground is approximately 5.29 feet.

## Pythagorean Theorem FAQS

##### Who discovered the Pythagorean Theorem?

The Pythagorean Theorem is named after the ancient Greek mathematician Pythagoras, who is credited with discovering the theorem.

##### What is the Pythagorean Theorem used for?

The Pythagorean Theorem has many practical applications in fields such as architecture, engineering, and physics. It is also an important tool in many areas of mathematics, including trigonometry and geometry.

##### How do you use the Pythagorean Theorem?

To use the Pythagorean Theorem, you need to identify the right triangle and its three sides. Then, you can plug in the lengths of the two legs into the equation c^2 = a^2 + b^2 and solve for the length of the hypotenuse.

##### Can the Pythagorean Theorem be used for non-right triangles?

No, the Pythagorean Theorem only applies to right triangles. For non-right triangles, other methods such as the Law of Cosines or Law of Sines are used to find the lengths of the sides.

##### Is the Pythagorean Theorem reversible?

Yes, the Pythagorean Theorem is reversible. If you know the length of the hypotenuse and one of the legs of a right triangle, you can use the theorem to find the length of the other leg.

##### Is the Pythagorean Theorem only applicable to triangles with whole number side lengths?

No, the Pythagorean Theorem is applicable to right triangles with any real number side lengths. It can be used to find the length of the hypotenuse or the length of either leg, regardless of whether the side lengths are whole numbers or not. Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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