A Right Triangle with Sides 6 cm, 8 cm, and 10 cm
This article will explore a right triangle with sides measuring 6 cm, 8 cm, and 10 cm. We'll delve into the properties of this triangle, its significance, and its relationship to the Pythagorean theorem.
Understanding the Triangle
A right triangle is a triangle where one of the angles measures 90 degrees. In this specific case, we have a triangle with sides of 6 cm, 8 cm, and 10 cm.
Key Properties:
- Hypotenuse: The longest side of a right triangle is called the hypotenuse. In this case, the hypotenuse is 10 cm long.
- Legs: The other two sides of the right triangle are called legs. These are the sides that form the right angle. Here, the legs are 6 cm and 8 cm long.
The Pythagorean Theorem
The Pythagorean theorem is a fundamental concept in geometry that states: "In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides."
Applying it to our triangle:
- Hypotenuse: 10 cm
- Leg 1: 6 cm
- Leg 2: 8 cm
Calculation:
- 10² = 6² + 8²
- 100 = 36 + 64
- 100 = 100
The equation holds true, proving that our triangle is indeed a right triangle.
Significance of This Triangle
This specific right triangle (with sides 6 cm, 8 cm, and 10 cm) is often referred to as a Pythagorean triple because its sides are whole numbers that satisfy the Pythagorean theorem. It's a common example used to illustrate the theorem and its applications.
Applications:
- Construction and Engineering: The Pythagorean theorem and Pythagorean triples are used in various construction and engineering applications, such as calculating distances, determining the strength of structures, and laying out foundations.
- Navigation: Understanding right triangles and the Pythagorean theorem is crucial in navigation, particularly for calculating distances and bearings.
- Mathematics: Pythagorean triples are studied extensively in number theory and geometry, exploring their properties and connections to other mathematical concepts.
Conclusion
The right triangle with sides 6 cm, 8 cm, and 10 cm is a perfect example of the Pythagorean theorem in action. This triangle demonstrates the relationship between the sides of a right triangle and its significance in various fields. Understanding this concept helps us comprehend the fundamental principles of geometry and its applications in the real world.
