Right Triangle Side and Angle Calculator with Points

Right Triangle Calculations:

\[ c = \sqrt{a^2 + b^2} \] \[ \theta = \arctan\left(\frac{opposite}{adjacent}\right) \]

Results:

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1. What is a Right Triangle Calculator?

This calculator determines whether three given points form a right triangle and calculates all side lengths and angles if they do. It uses coordinate geometry and trigonometric functions to perform these calculations.

2. How Does the Calculator Work?

The calculator uses these mathematical formulas:

\[ \text{Distance between points} = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} \] \[ \text{Angle} = \arctan\left(\frac{\Delta y}{\Delta x}\right) \]

Where:

\( (x_1,y_1) \), \( (x_2,y_2) \), \( (x_3,y_3) \) — Coordinate points
\( \Delta x \), \( \Delta y \) — Differences in x and y coordinates

Explanation: The calculator first checks if the points satisfy the Pythagorean theorem (a² + b² = c²) to verify if they form a right triangle.

3. Importance of Triangle Calculations

Details: Right triangle calculations are fundamental in geometry, physics, engineering, and computer graphics. They're used in navigation, construction, and many real-world applications.

4. Using the Calculator

Tips: Enter the (x,y) coordinates for three points. The calculator will determine if they form a right triangle and display all sides and angles if they do.

5. Frequently Asked Questions (FAQ)

Q1: What if my points don't form a right triangle?
A: The calculator will notify you if the points don't form a right triangle according to the Pythagorean theorem.

Q2: How precise are the calculations?
A: Calculations are precise to 2 decimal places, with a small tolerance for floating-point comparisons.

Q3: Can I use negative coordinates?
A: Yes, the calculator works with any real number coordinates.

Q4: What units are used?
A: The units depend on your coordinate system. Side lengths are in the same units as your coordinates.

Q5: How are angles measured?
A: Angles are measured in degrees, with 0° along the positive x-axis increasing counterclockwise.