What is the Pythagorean triplet?

A Pythagorean triplet consists of three positive integers a, b, and c, such that $$a^2 + b^2 = c^2$$ . Example: (3, 4, 5).

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

No, the Pythagorean Theorem only applies to right triangles.

What is the value of c if a = 6 and b = 8 in a right triangle?

Using the Pythagorean Theorem: $$6^2 + 8^2 = c^2$$ , so $$36 + 64 = c^2$$ , thus $$c = 10$$ .

What is the error in the statement: a^2 + b^3 = c^4?

The correct form of the Pythagorean Theorem is $$a^2 + b^2 = c^2$$ , not $$a^2 + b^3 = c^4$$ .

If the hypotenuse is 25 and one leg is 20, what is the length of the other leg?

Using the Pythagorean Theorem: $$20^2 + b^2 = 25^2$$ , so $$400 + b^2 = 625$$ , thus $$b = 15$$ .

What is the distance formula derived from the Pythagorean Theorem?

The distance formula between two points (x1, y1) and (x2, y2) is: $$d = \text{sqrt}((x2 - x1)^2 + (y2 - y1)^2)$$ .

What is the significance of the Pythagorean Theorem in real life?

The Pythagorean Theorem is used in various fields such as construction, navigation, and physics to calculate distances and angles.

Pythagorean Theorem Flashcards

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14 questions

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1.

FLASHCARD QUESTION

Front

What is the Pythagorean Theorem?

Back

2.

FLASHCARD QUESTION

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

3.

FLASHCARD QUESTION

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

4.

FLASHCARD QUESTION

Front

If a right triangle has legs of lengths 3 and 4, what is the length of the hypotenuse?

Back

5.

FLASHCARD QUESTION

Front

What is the formula to find the length of a missing side in a right triangle?

Back

6.

FLASHCARD QUESTION

Front

What is the relationship between the sides of a 5-12-13 triangle?

Back

7.

FLASHCARD QUESTION

Front

If the lengths of the sides of a right triangle are 8 and 15, what is the length of the hypotenuse?

Back

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