First Inner Side Of Concave Quadrilateral Calculator

Formula Used:

\[ \text{First Inner Side} = \sqrt{\text{First Outer Side}^2 + \text{Outer Diagonal}^2 - (2 \times \text{First Outer Side} \times \text{Outer Diagonal} \times \cos(\text{Second Acute Angle}))} \]

First Inner Side:

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1. What is the First Inner Side of Concave Quadrilateral?

The First Inner Side of a Concave Quadrilateral is the first innermost side of the Concave Quadrilateral. It is calculated using the Law of Cosines based on the first outer side, outer diagonal, and the second acute angle.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{First Inner Side} = \sqrt{\text{First Outer Side}^2 + \text{Outer Diagonal}^2 - (2 \times \text{First Outer Side} \times \text{Outer Diagonal} \times \cos(\text{Second Acute Angle}))} \]

Where:

First Outer Side — First outermost side of the Concave Quadrilateral (m)
Outer Diagonal — Diagonal lying outside the region of the Concave Quadrilateral (m)
Second Acute Angle — Angle formed between second outer and second inner side (rad)

Explanation: This formula applies the Law of Cosines to find the first inner side using the given geometric parameters.

3. Importance of First Inner Side Calculation

Details: Calculating the first inner side is essential for determining the complete geometry of a concave quadrilateral, which is important in various fields including architecture, engineering, and computer graphics.

4. Using the Calculator

Tips: Enter the first outer side and outer diagonal in meters, and the second acute angle in radians. All values must be positive, with the angle between 0 and π/2 radians.

5. Frequently Asked Questions (FAQ)

Q1: What is a concave quadrilateral?
A: A concave quadrilateral is a four-sided polygon with at least one interior angle greater than 180 degrees, causing at least one vertex to point inward.

Q2: Why use radians for angle measurement?
A: Radians are the standard unit for angle measurement in mathematical calculations involving trigonometric functions, providing more accurate results.

Q3: Can this formula be used for convex quadrilaterals?
A: This specific formula is designed for concave quadrilaterals with the given geometric configuration and may not apply directly to convex quadrilaterals.

Q4: What if the angle is in degrees?
A: Convert degrees to radians by multiplying by π/180 before entering the value, as the calculator expects angle input in radians.

Q5: Are there any limitations to this calculation?
A: The calculation assumes standard geometric properties and may not be accurate for quadrilaterals with extreme proportions or non-standard configurations.