Triangle Calculator by Coordinates

Triangle Calculations:

\[ \text{Area} = \frac{1}{2} |(x_A(y_B - y_C) + x_B(y_C - y_A) + x_C(y_A - y_B))| \]

Side AB:

Side BC:

Side CA:

Angle A:

Angle B:

Angle C:

Area:

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1. What is the Triangle Calculator by Coordinates?

This calculator determines all properties of a triangle (side lengths, angles, area) when given the coordinates of its three vertices in a 2D plane.

2. How Does the Calculator Work?

The calculator uses these mathematical formulas:

\[ \text{Distance between points} = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} \] \[ \text{Area} = \frac{1}{2} |(x_A(y_B - y_C) + x_B(y_C - y_A) + x_C(y_A - y_B))| \] \[ \text{Angles via Law of Cosines} = \cos^{-1}\left(\frac{b^2 + c^2 - a^2}{2bc}\right) \]

Where:

\( (x_A,y_A), (x_B,y_B), (x_C,y_C) \) — Vertex coordinates
\( a, b, c \) — Lengths of sides opposite vertices A, B, C respectively

3. Importance of Triangle Calculations

Details: Calculating triangle properties from coordinates is fundamental in geometry, computer graphics, surveying, and various engineering applications.

4. Using the Calculator

Tips: Enter the (x,y) coordinates for all three vertices of the triangle. The calculator will compute side lengths, angles, and area.

5. Frequently Asked Questions (FAQ)

Q1: What if the points are colinear?
A: The calculator will show an area of 0, indicating the points don't form a valid triangle.

Q2: Does the order of points matter?
A: No, the calculator works regardless of the order you enter the points.

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

Q4: How precise are the calculations?
A: Results are rounded to 2 decimal places for lengths/area, 1 decimal place for angles.

Q5: What coordinate system is used?
A: Standard Cartesian coordinate system (x horizontal, y vertical).