Angle A Of Cyclic Quadrilateral Calculator

Angle A of Cyclic Quadrilateral Formula:

\[ \angle A = \arccos\left(\frac{Sa^2 + Sd^2 - Sb^2 - Sc^2}{2 \times ((Sa \times Sd) + (Sb \times Sc))}\right) \]

Side A of Cyclic Quadrilateral:

Side D of Cyclic Quadrilateral:

Side B of Cyclic Quadrilateral:

Side C of Cyclic Quadrilateral:

Angle A of Cyclic Quadrilateral:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Angle A of Cyclic Quadrilateral?

Angle A of a cyclic quadrilateral is the angle formed between two adjacent sides (Side A and Side D) of a quadrilateral inscribed in a circle. In a cyclic quadrilateral, opposite angles sum to 180 degrees.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \angle A = \arccos\left(\frac{Sa^2 + Sd^2 - Sb^2 - Sc^2}{2 \times ((Sa \times Sd) + (Sb \times Sc))}\right) \]

Where:

\( Sa \) — Side A of Cyclic Quadrilateral (m)
\( Sd \) — Side D of Cyclic Quadrilateral (m)
\( Sb \) — Side B of Cyclic Quadrilateral (m)
\( Sc \) — Side C of Cyclic Quadrilateral (m)
\( \arccos \) — Inverse cosine function

Explanation: This formula calculates angle A using the lengths of all four sides of the cyclic quadrilateral through trigonometric relationships.

3. Importance of Angle Calculation

Details: Calculating angles in cyclic quadrilaterals is essential in geometry, engineering, and architecture for determining properties of circularly inscribed quadrilaterals and solving related geometric problems.

4. Using the Calculator

Tips: Enter all four side lengths in meters. All values must be positive numbers greater than zero. The calculator will compute angle A in degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is a cyclic quadrilateral?
A: A cyclic quadrilateral is a four-sided polygon where all vertices lie on a single circle.

Q2: Why is this formula used for angle calculation?
A: This formula derives from the cosine rule applied to the cyclic quadrilateral's properties, relating side lengths to the angles.

Q3: What are the valid input ranges?
A: All side lengths must be positive numbers. The calculated ratio must be between -1 and 1 for valid arccos computation.

Q4: Can this calculator handle decimal inputs?
A: Yes, the calculator accepts decimal values with up to 4 decimal places precision.

Q5: What units does the calculator use?
A: The calculator uses meters for side lengths and returns angle in degrees.