Final answer:
Using the Pythagorean theorem, which relates the lengths of the legs of a right triangle to its hypotenuse, we find that the length of the hypotenuse is 85 inches when the legs are 36 and 77 inches long.
Step-by-step explanation:
To find the length of the hypotenuse of a right triangle when the lengths of the legs are given, we 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). Using the formula c = √(a² + b²), we can calculate the hypotenuse for the triangle with legs of 36 inches and 77 inches.
- First, square the lengths of the legs: 36² + 77².
- Calculate the squares: 1296 + 5929
- Add the squares: 7225.
- Find the square root of the sum: c = √7225.
- The hypotenuse is: 85 inches.
Therefore, the length of the hypotenuse is 85 inches (Option C).