Quadrilateral Angles From Sides Calculator

Quadrilateral Angle Calculation Methods:

\[ \text{1. Law of Cosines: } \cos(A) = \frac{b^2 + d^2 - D_1^2}{2bd} \] \[ \text{2. Triangle Division: Divide quadrilateral into two triangles and calculate angles} \]

Side a:

units

Side b:

units

Side c:

units

Side d:

units

Diagonal (optional):

units

Angle Unit:

Angle A:

Angle B:

Angle C:

Angle D:

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1. What is Quadrilateral Angle Calculation?

This calculator determines the interior angles of a quadrilateral when all four side lengths are known. It uses either the Law of Cosines on the diagonals or divides the quadrilateral into triangles to calculate the angles.

2. How Does the Calculator Work?

The calculator uses two main methods:

\[ \text{1. Law of Cosines: } \cos(A) = \frac{b^2 + d^2 - D_1^2}{2bd} \] \[ \text{2. Triangle Division: Divide quadrilateral into two triangles and calculate angles} \]

Where:

\( a, b, c, d \) — Sides of the quadrilateral
\( D_1 \) — Diagonal between sides b and d
\( A \) — Angle between sides b and d

Explanation: The calculator first determines the diagonal length (if not provided), then uses the Law of Cosines to find the angles.

3. Importance of Angle Calculation

Details: Knowing the angles of a quadrilateral is essential in geometry, architecture, engineering, and various design applications where precise measurements are required.

4. Using the Calculator

Tips: Enter all four side lengths in consistent units. You may optionally provide one diagonal length for more accurate results. Select whether you want angles in degrees or radians.

5. Frequently Asked Questions (FAQ)

Q1: Can this calculator work for any quadrilateral?
A: It works for most simple quadrilaterals, but results may be inaccurate for complex or self-intersecting quadrilaterals.

Q2: Why might I need to provide a diagonal?
A: Providing a diagonal increases accuracy since quadrilaterals with the same side lengths can have different angles (they're not rigid).

Q3: What if my quadrilateral is concave?
A: The calculator should still work, but one angle will be greater than 180° (or π radians).

Q4: How precise are the results?
A: Results are precise to two decimal places, but actual precision depends on the accuracy of your input measurements.

Q5: Can I use this for cyclic quadrilaterals?
A: Yes, but for cyclic quadrilaterals, you might get more accurate results using the supplementary angle property.