What is the significance of the 'Pythagorean theorem' in modern mathematics?

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Question: What is the significance of the \'Pythagorean theorem\' in modern mathematics?

Options:

Correct Answer: It establishes a relationship between the sides of a right triangle.

Solution:

The Pythagorean theorem establishes a fundamental relationship between the sides of a right triangle.

What is the significance of the 'Pythagorean theorem' in modern mathematics?

What is the significance of the 'Pythagorean theorem' in modern mathematics?

Step 1: Understand that the Pythagorean theorem applies to right triangles, which have one angle that is 90 degrees.
Step 2: The theorem 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.
Step 3: This relationship can be written as the formula: a² + b² = c², where 'c' is the length of the hypotenuse and 'a' and 'b' are the lengths of the other two sides.
Step 4: The significance of the theorem in modern mathematics is that it helps in solving problems related to geometry, trigonometry, and even in fields like physics and engineering.
Step 5: It is also used in real-world applications, such as construction, navigation, and computer graphics, making it a crucial concept in various disciplines.

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