1. What is a 45-45-90 Triangle Calculator?

Definition: This calculator computes the hypotenuse of a 45-45-90 right triangle based on the length of its legs.

Purpose: It helps students, engineers, and construction professionals quickly solve for the hypotenuse in these special right triangles.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \text{hyp} \) — Hypotenuse length (meters)
• \( \text{leg} \) — Leg length (meters)
• \( \sqrt{2} \) — Approximately 1.41421

Explanation: In a 45-45-90 triangle, both legs are equal, and the hypotenuse is always √2 times the length of either leg.

3. Importance of 45-45-90 Triangles

Details: These special right triangles are fundamental in geometry, construction, and engineering, often appearing in diagonal measurements of squares.

4. Using the Calculator

Tips: Simply enter the length of one leg in meters. The calculator will automatically compute the hypotenuse.

5. Frequently Asked Questions (FAQ)

Q1: What makes a 45-45-90 triangle special?
A: It's an isosceles right triangle where both acute angles are 45° and the sides have a consistent ratio of 1:1:√2.

Q2: Can I calculate the legs from the hypotenuse?
A: Yes, the leg length equals the hypotenuse divided by √2.

Q3: Where are these triangles commonly used?
A: In construction for diagonal measurements, in engineering for force calculations, and in various design applications.

Q4: What if my triangle isn't exactly 45-45-90?
A: This calculator only works for perfect 45-45-90 triangles. For others, use the Pythagorean theorem.

Q5: How precise is the √2 calculation?
A: The calculator uses double-precision floating point arithmetic (about 15 decimal digits of precision).