1. What is the Hypotenuse of Isosceles Right Triangle?

The hypotenuse of an isosceles right triangle is the longest side opposite the right angle. In an isosceles right triangle, the two legs are equal in length, and the hypotenuse can be calculated using the Pythagorean theorem.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( H \) — Hypotenuse of Isosceles Right Triangle (m)
• \( S \) — Legs of Isosceles Right Triangle (m)
• \( \sqrt{2} \) — Square root of 2 (approximately 1.414214)

Explanation: This formula is derived from the Pythagorean theorem where both legs are equal (a = b = S), so \( H = \sqrt{S^2 + S^2} = \sqrt{2S^2} = S\sqrt{2} \).

3. Importance of Hypotenuse Calculation

Details: Calculating the hypotenuse is essential in geometry, construction, engineering, and various practical applications where right triangles are involved. It helps determine distances, angles, and dimensions in triangular structures.

4. Using the Calculator

Tips: Enter the length of one leg in meters. The value must be positive and valid. The calculator will compute the hypotenuse using the formula \( H = \sqrt{2} \times S \).

5. Frequently Asked Questions (FAQ)

Q1: Why is the hypotenuse longer than the legs?
A: According to the Pythagorean theorem, the hypotenuse is always the longest side in a right triangle as it's opposite the right angle.

Q2: What is the approximate value of √2?
A: The square root of 2 is approximately 1.414213562, which is an irrational number.

Q3: Can this formula be used for any right triangle?
A: This specific formula \( H = \sqrt{2} \times S \) applies only to isosceles right triangles where both legs are equal. For other right triangles, use the general Pythagorean theorem.

Q4: What are some practical applications?
A: This calculation is used in construction, carpentry, navigation, computer graphics, and various engineering fields where right angles and equal sides are involved.

Q5: How accurate is the calculation?
A: The calculation is mathematically exact. The accuracy of the result depends on the precision of the input value and the computational precision of the calculator.