Which formula is used to find the hypotenuse of a right triangle?

Which formula is used to find the hypotenuse of a right triangle?

• A. Pythagorean theorem: a^2 + b^2 = c^2
• B. c = a + b
• C. c = a - b
• D. c = 2ab

Answer: (A)

The Pythagorean theorem is a fundamental principle used to determine the length of the hypotenuse in a right triangle. In this theorem, a and b represent the lengths of the two legs of the triangle, while c denotes the length of the hypotenuse. The formula states that the sum of the squares of the legs equals the square of the hypotenuse, expressed mathematically as \( a^2 + b^2 = c^2 \). When you apply this formula, if you know the lengths of the two legs, you can easily calculate the hypotenuse by rearranging the equation to \( c = \sqrt{a^2 + b^2} \). This relationship is foundational in geometry and is essential for solving various problems involving right triangles. The other choices do not represent the relationship needed to compute the hypotenuse in a right triangle, which is why they do not apply in this context.

The Pythagorean theorem is a fundamental principle used to determine the length of the hypotenuse in a right triangle. In this theorem, a and b represent the lengths of the two legs of the triangle, while c denotes the length of the hypotenuse. The formula states that the sum of the squares of the legs equals the square of the hypotenuse, expressed mathematically as ( a^2 + b^2 = c^2 ).

When you apply this formula, if you know the lengths of the two legs, you can easily calculate the hypotenuse by rearranging the equation to ( c = \sqrt{a^2 + b^2} ). This relationship is foundational in geometry and is essential for solving various problems involving right triangles. The other choices do not represent the relationship needed to compute the hypotenuse in a right triangle, which is why they do not apply in this context.