Legs Of Isosceles Right Triangle Given Hypotenuse Calculator

Formula Used:

\[ \text{Legs of Isosceles Right Triangle} = \frac{\text{Hypotenuse of Isosceles Right Triangle}}{\sqrt{2}} \]

Legs of Isosceles Right Triangle:

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1. What is the Legs of Isosceles Right Triangle Formula?

The formula calculates the length of the equal legs in an isosceles right triangle when the hypotenuse is known. In an isosceles right triangle, the two legs are equal in length and form a right angle.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Legs} = \frac{\text{Hypotenuse}}{\sqrt{2}} \]

Where:

\( \text{Legs} \) — Length of each equal side of the isosceles right triangle (meters)
\( \text{Hypotenuse} \) — Length of the hypotenuse (meters)
\( \sqrt{2} \) — Square root of 2 (approximately 1.414213562)

Explanation: This formula is derived from the Pythagorean theorem, where in an isosceles right triangle, the hypotenuse equals the leg length multiplied by √2.

3. Importance of Legs Calculation

Details: Calculating the leg lengths is essential in geometry, construction, and various engineering applications where isosceles right triangles are used. It helps determine dimensions and proportions in structural designs.

4. Using the Calculator

Tips: Enter the hypotenuse length in meters. The value must be positive and greater than zero. The calculator will compute the length of each equal leg.

5. Frequently Asked Questions (FAQ)

Q1: Why divide by √2 to find the legs?
A: In an isosceles right triangle, the relationship between the hypotenuse and legs is given by hypotenuse = leg × √2, so solving for leg gives leg = hypotenuse / √2.

Q2: What are the properties of an isosceles right triangle?
A: It has two equal sides, one right angle (90°), and two equal angles of 45° each. The hypotenuse is always the longest side.

Q3: Can this formula be used for any right triangle?
A: No, this specific formula only applies to isosceles right triangles where the two legs are equal. For other right triangles, use the standard Pythagorean theorem.

Q4: What is the approximate value of √2?
A: √2 is approximately 1.414213562. This irrational number represents the ratio between the hypotenuse and leg in an isosceles right triangle.

Q5: How accurate are the calculations?
A: The calculator provides results with 6 decimal places precision, which is sufficient for most practical applications in geometry and engineering.