1. What is the Long Diagonal of Rhombus given Inradius?

The Long Diagonal of a Rhombus given Inradius is calculated using the inradius and acute angle of the rhombus. This formula provides a geometric relationship between the inscribed circle and the diagonal lengths of the rhombus.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• Inradius — The radius of the circle inscribed inside the rhombus (m)
• Acute Angle — The acute angle of the rhombus in degrees (°)
• sin — Trigonometric sine function

Explanation: The formula derives from the geometric properties of rhombus and its inscribed circle, using trigonometric relationships between the angles and diagonals.

3. Importance of Long Diagonal Calculation

Details: Calculating the long diagonal is essential in geometry problems, architectural design, and various engineering applications where rhombus shapes are used. It helps in determining the overall dimensions and proportions of rhombus-based structures.

4. Using the Calculator

Tips: Enter the inradius in meters and the acute angle in degrees. The angle must be between 0° and 90° (exclusive), and the inradius must be a positive value.

5. Frequently Asked Questions (FAQ)

Q1: What is a rhombus?
A: A rhombus is a quadrilateral with all four sides of equal length, opposite sides parallel, and opposite angles equal.

Q2: What is the inradius of a rhombus?
A: The inradius is the radius of the largest circle that can be inscribed inside the rhombus, tangent to all four sides.

Q3: Can this formula be used for any rhombus?
A: Yes, this formula applies to all rhombuses as long as the acute angle and inradius are known.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of rhombuses, given accurate input values.

Q5: What are practical applications of this calculation?
A: This calculation is used in various fields including architecture, engineering design, crystallography, and geometric modeling.