1. What is a 45-Degree Right Triangle?

A 45-degree right triangle (isosceles right triangle) is a special right triangle where the two legs are equal in length and the angles opposite them are both 45 degrees. The remaining angle is 90 degrees.

2. How Does the Calculator Work?

The calculator uses the following formulas:

Where:

• \( a \) — Length of both legs (equal sides)
• \( h \) — Length of the hypotenuse
• \( \sqrt{2} \) — Approximately 1.41421

Explanation: In a 45-45-90 triangle, the hypotenuse is always √2 times the length of each leg.

3. Importance of 45-Degree Right Triangles

Details: These triangles are fundamental in geometry, trigonometry, and various applications including construction, engineering, and computer graphics. They represent the simplest case of an isosceles right triangle.

4. Using the Calculator

Tips: Enter the length of either leg in any units. The calculator will compute the hypotenuse in the same units. The value must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Why is the hypotenuse √2 times the leg?
A: This comes from the Pythagorean theorem: \( h = \sqrt{a^2 + a^2} = \sqrt{2a^2} = a\sqrt{2} \).

Q2: Can I calculate the legs from the hypotenuse?
A: Yes, the leg length would be \( a = h/\sqrt{2} \).

Q3: What are some real-world applications?
A: Used in diagonal measurements of squares, roof framing, and determining screen sizes (diagonal measurement).

Q4: How precise is the calculation?
A: The calculation is mathematically exact. The displayed result is rounded to 4 decimal places for readability.

Q5: Can this calculator work for other right triangles?
A: No, this is specifically for 45-45-90 triangles. Other right triangles require different calculations.