Diagonal 2 of Quadrilateral Calculator

Diagonal 2 of Quadrilateral Formula:

\[ d2 = \sqrt{Sb^2+Sc^2-(2 \times Sb \times Sc \times \cos(\angle C))} \]

Diagonal 2 of Quadrilateral:

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1. What is the Diagonal 2 of Quadrilateral Formula?

The Diagonal 2 of Quadrilateral formula calculates the length of the second diagonal in a quadrilateral using the lengths of two adjacent sides and the included angle between them. This formula is derived from the Law of Cosines applied to the triangle formed by the two sides and the diagonal.

2. How Does the Calculator Work?

The calculator uses the Diagonal 2 formula:

\[ d2 = \sqrt{Sb^2+Sc^2-(2 \times Sb \times Sc \times \cos(\angle C))} \]

Where:

\( d2 \) — Diagonal 2 of Quadrilateral (m)
\( Sb \) — Side B of Quadrilateral (m)
\( Sc \) — Side C of Quadrilateral (m)
\( \angle C \) — Angle C of Quadrilateral between side B and side C (radians)

Explanation: The formula applies the Law of Cosines to find the diagonal length opposite to the given angle, using the two adjacent sides.

3. Importance of Diagonal Calculation

Details: Calculating diagonals is essential in geometry for determining quadrilateral properties, area calculations, and in various engineering applications where quadrilateral shapes are involved.

4. Using the Calculator

Tips: Enter side lengths in meters and angle in degrees. All values must be positive (sides > 0, angle between 0-360 degrees).

5. Frequently Asked Questions (FAQ)

Q1: What types of quadrilaterals does this formula work for?
A: This formula works for any quadrilateral where you know two adjacent sides and the included angle between them.

Q2: Why do we need to convert angle from degrees to radians?
A: Trigonometric functions in mathematical calculations typically use radians, so conversion is necessary for accurate results.

Q3: Can this formula be used for all diagonals in a quadrilateral?
A: This specific formula calculates the diagonal opposite to the given angle. For the other diagonal, you would need different side lengths and angles.

Q4: What are practical applications of this calculation?
A: This calculation is used in construction, engineering design, land surveying, and computer graphics where quadrilateral shapes are common.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the input values. The practical accuracy depends on the precision of the measured side lengths and angles.