When finding the length of the hypotenuse of a right triangle with legs of lengths $a$ and $b$, which formula should you use?

• A. $c=a^2-b^2$
• B. $c=a^2+b^2$
• C. $c=\sqrt{a^2+b^2}$
• D. $c=\sqrt{a^2-b^2}$

Answer: (C)

Verified step by step guidance

1. Recall that in a right triangle, the hypotenuse is the side opposite the right angle and is the longest side.
2. Use the Pythagorean theorem, which states that the square of the hypotenuse length \(c\) is equal to the sum of the squares of the other two legs \(a\) and \(b\).
3. Write the Pythagorean theorem formula as \(c^2 = a^2 + b^2\).
4. To find the length of the hypotenuse \(c\), take the square root of both sides of the equation, resulting in \(c = \sqrt{a^2 + b^2}\).
5. Avoid subtracting the squares of the legs, as that does not apply to the Pythagorean theorem for right triangles.