The Pythagorean Theorem is a fundamental concept in geometry that relates the sides of a right triangle. It states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides, which are called legs. Mathematically, this can be expr...
a² + b² = c²
Where:
- a and b are the lengths of the legs of the right triangle.
- c is the length of the hypotenuse.
Applying the Pythagorean Theorem to the Problem
We are given the lengths of the legs of a right triangle as 33 inches and 56 inches. We need to find the length of the hypotenuse. Let's use the Pythagorean Theorem to solve this:
- Assign values to variables:
- a = 33 inches
- b = 56 inches
- c = ? (hypotenuse)
- Substitute the values into the Pythagorean Theorem equation:
33² + 56² = c²
- Calculate the squares:
1089 + 3136 = c²
- Add the numbers on the left side:
4225 = c²
- Isolate c by taking the square root of both sides:
√4225 = √c²
- Solve for c:
65 = c
The Solution
Therefore, the length of the hypotenuse of the right triangle is 65 inches.
Conclusion
By using the Pythagorean Theorem, we have successfully calculated the length of the hypotenuse of a right triangle given the lengths of its legs. This demonstrates the powerful application of the theorem in solving problems involving right triangles.