Penerapan Teorema Pythagoras dalam Menghitung Panjang Hipotenusa Segitiga Siku-Siku

The Pythagorean theorem is a fundamental concept in geometry that establishes a relationship between the sides of a right triangle. This theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides, known as the legs. This principle has numerous applications in various fields, including engineering, architecture, and navigation. One of the most common applications of the Pythagorean theorem is in calculating the length of the hypotenuse of a right triangle, given the lengths of the two legs. This article will delve into the practical application of the Pythagorean theorem in determining the hypotenuse of a right triangle, providing a step-by-step guide and illustrative examples.

Understanding the Pythagorean Theorem

The Pythagorean theorem is represented by the equation: a² + b² = c², where 'a' and 'b' are the lengths of the legs of the right triangle, and 'c' is the length of the hypotenuse. This equation implies that if we know the lengths of the two legs, we can calculate the length of the hypotenuse by taking the square root of the sum of the squares of the legs.

Applying the Theorem to Calculate the Hypotenuse

To calculate the length of the hypotenuse using the Pythagorean theorem, we need to follow these steps:

1. Identify the legs and the hypotenuse: In a right triangle, the hypotenuse is always the longest side and is opposite the right angle. The other two sides are the legs.

2. Square the lengths of the legs: Multiply each leg's length by itself.

3. Add the squares of the legs: Sum the results obtained in step 2.

4. Take the square root of the sum: Find the square root of the sum obtained in step 3. This will give you the length of the hypotenuse.

Illustrative Examples

Let's consider a few examples to illustrate the application of the Pythagorean theorem in calculating the hypotenuse:

Example 1:

Suppose we have a right triangle with legs of length 3 cm and 4 cm. To find the length of the hypotenuse, we can apply the Pythagorean theorem:

a² + b² = c²

3² + 4² = c²

9 + 16 = c²

25 = c²

c = √25 = 5 cm

Therefore, the length of the hypotenuse is 5 cm.

Example 2:

Consider another right triangle with legs of length 5 m and 12 m. Using the Pythagorean theorem, we can calculate the hypotenuse:

a² + b² = c²

5² + 12² = c²

25 + 144 = c²

169 = c²

c = √169 = 13 m

Hence, the length of the hypotenuse is 13 m.

Conclusion

The Pythagorean theorem is a powerful tool for calculating the length of the hypotenuse of a right triangle. By understanding the theorem and following the steps outlined above, we can easily determine the hypotenuse given the lengths of the legs. This principle has wide-ranging applications in various fields, making it an essential concept in mathematics and related disciplines.