1. What is an Isosceles Right Triangle?

An isosceles right triangle is a special right triangle where the two legs are of equal length and the angles opposite the legs are both 45 degrees. It combines the properties of both isosceles triangles and right triangles.

2. How Does the Calculator Work?

The calculator uses the isosceles right triangle formula:

Where:

• Leg — Length of the equal sides (same units)
• √2 — Approximately 1.41421
• Hypotenuse — Longest side opposite the right angle

Explanation: This formula comes directly from the Pythagorean theorem applied to a triangle with two equal sides.

3. Properties of Isosceles Right Triangle

Details: In an isosceles right triangle:

• Two sides (legs) are equal
• Two angles are equal (45° each)
• One right angle (90°)
• Area = (leg × leg) / 2
• Perimeter = 2 × leg + hypotenuse

4. Using the Calculator

Tips: Simply enter the length of one leg to calculate the hypotenuse. The leg must be a positive number.

5. Frequently Asked Questions (FAQ)

Q1: What's the ratio of sides in an isosceles right triangle?
A: The sides are in the ratio 1:1:√2 (leg:leg:hypotenuse).

Q2: How do you find the area?
A: Area = (leg²)/2 or (hypotenuse²)/4.

Q3: Can this calculator find the legs if I know the hypotenuse?
A: No, this version only calculates hypotenuse from leg. The reverse would be leg = hypotenuse/√2.

Q4: What units does this calculator use?
A: Any consistent length units (cm, inches, etc.) as long as the same unit is used for all measurements.

Q5: Where are isosceles right triangles used?
A: Commonly in architecture, engineering, and design where 45° angles are needed, and in trigonometry problems.