Angle And Side Length Calculator From Points

Side Length Formula:

\[ Side = \sqrt{(x2 - x1)^2 + (y2 - y1)^2} \]

Side Length:

Angle (degrees):

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1. What is the Angle and Side Length Calculator?

This calculator determines the length of a side between two points and the angle of that side relative to the horizontal axis using their Cartesian coordinates.

2. How Does the Calculator Work?

The calculator uses the distance formula:

\[ Side = \sqrt{(x2 - x1)^2 + (y2 - y1)^2} \]

And the angle formula:

\[ \theta = \arctan\left(\frac{y2 - y1}{x2 - x1}\right) \]

Where:

\( (x1, y1) \) — Coordinates of the first point
\( (x2, y2) \) — Coordinates of the second point
\( \theta \) — Angle in degrees from the horizontal axis

3. Importance of Coordinate Calculations

Details: Calculating distances and angles between points is fundamental in geometry, physics, engineering, and computer graphics applications.

4. Using the Calculator

Tips: Enter the Cartesian coordinates of two points to calculate the distance between them and the angle of the line connecting them relative to the positive x-axis.

5. Frequently Asked Questions (FAQ)

Q1: What coordinate system does this use?
A: The calculator uses standard Cartesian coordinates with x increasing to the right and y increasing upwards.

Q2: How is the angle measured?
A: The angle is measured in degrees from the positive x-axis, with positive angles going counter-clockwise.

Q3: Can I use negative coordinates?
A: Yes, the calculator works with both positive and negative coordinate values.

Q4: What's the range of the angle output?
A: The angle ranges from -180° to +180° (or 0° to 360° depending on implementation).

Q5: How precise are the calculations?
A: Results are rounded to 4 decimal places for side length and 2 decimal places for angles.