Understanding the hypotenuse is fundamental in geometry, especially when dealing with right-angled triangles. If you’re searching for “hypotenuse meaning in Hindi,” you’ve come to the right place. This article will delve into the definition, significance, and practical applications of the hypotenuse, clarifying its meaning in Hindi and exploring related concepts.
Understanding the Term “Hypotenuse”
In any right-angled triangle, the hypotenuse is the longest side, always opposite the right angle (90-degree angle). In Hindi, the hypotenuse is referred to as “कर्ण” (karn). Remembering this simple definition is key to solving many geometric problems.
Hypotenuse in the Pythagorean Theorem
The hypotenuse plays a crucial role in the Pythagorean theorem, a fundamental concept in geometry. This theorem states that the square of the hypotenuse (karn) is equal to the sum of the squares of the other two sides (legs). Mathematically, it is represented as a² + b² = c², where ‘c’ represents the length of the hypotenuse, and ‘a’ and ‘b’ represent the lengths of the other two sides.
Practical Applications of the Hypotenuse
Understanding the hypotenuse isn’t just theoretical; it has various practical applications. From calculating distances in navigation and construction to determining the height of buildings and understanding trigonometric ratios, the concept of the hypotenuse is widely used in various fields.
How to Find the Length of the Hypotenuse?
You can easily calculate the length of the hypotenuse using the Pythagorean theorem if you know the lengths of the other two sides. Conversely, if you know the length of the hypotenuse and one of the other sides, you can find the length of the remaining side using the same theorem.
Hypotenuse and Trigonometry
The hypotenuse is also central to trigonometric functions like sine, cosine, and tangent. These functions define the relationships between the angles and sides of a right-angled triangle. For instance, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.
Conclusion
The hypotenuse, known as “कर्ण” (karn) in Hindi, is the longest side of a right-angled triangle, opposite the right angle. Its significance is highlighted by its role in the Pythagorean theorem and trigonometric functions, making it a fundamental concept in geometry and its practical applications. Understanding the hypotenuse opens doors to solving various geometrical problems and understanding real-world scenarios.
FAQ
- What is the hypotenuse in a right triangle? The hypotenuse is the longest side, opposite the right angle.
- What is the Hindi word for hypotenuse? It’s “कर्ण” (karn).
- How is the hypotenuse related to the Pythagorean theorem? The square of the hypotenuse is equal to the sum of the squares of the other two sides.
- Why is the hypotenuse important? It’s crucial for calculations involving right-angled triangles, including finding lengths and understanding trigonometric functions.
- Can the hypotenuse be shorter than the other sides? No, it’s always the longest side.
- What are some real-world applications of the hypotenuse? Navigation, construction, surveying, and understanding wave patterns.
- How can I calculate the length of the hypotenuse? Use the Pythagorean theorem: a² + b² = c², where ‘c’ is the hypotenuse.
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