What is the value of the hypotenuse in a right triangle if the other two sides are 3 and 4?

To determine the length of the hypotenuse in a right triangle when the lengths of the other two sides are known, you can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).

In this case, the lengths of the two sides are 3 and 4. According to the Pythagorean theorem, you calculate the hypotenuse as follows:

1. Square the lengths of the two sides:

   • ( a^2 = 3^2 = 9 )
   • ( b^2 = 4^2 = 16 )

2. Add these two squares together:

   • ( a^2 + b^2 = 9 + 16 = 25 )

3. Take the square root of the sum to find the length of the hypotenuse:

   • ( c = \sqrt{25} = 5 )

Therefore, the value of the hypotenuse in this right triangle is 5. This result confirms the correct answer is indeed 5, which is derived directly