1. What is the Inradius of Rhombus?

The Inradius of Rhombus is defined as the radius of the circle which is inscribed inside the Rhombus. It represents the distance from the center of the inscribed circle to any side of the rhombus.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_i \) — Inradius of Rhombus (m)
• \( P \) — Perimeter of Rhombus (m)
• \( \angle_{Acute} \) — Acute Angle of Rhombus (radians)

Explanation: This formula calculates the inradius based on the perimeter and the acute angle of the rhombus, using trigonometric relationships.

3. Importance of Inradius Calculation

Details: Calculating the inradius is important in geometry for determining the size of the largest circle that can fit inside a rhombus, which has applications in various engineering and design fields.

4. Using the Calculator

Tips: Enter the perimeter in meters and the acute angle in degrees. The angle must be between 0 and 90 degrees, and the perimeter must be positive.

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: Why is the sine function used in this formula?
A: The sine function relates the acute angle to the ratio of sides in the right triangles formed by the diagonals of the rhombus.

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

Q4: What units should I use for inputs?
A: Perimeter should be in meters and angle in degrees. The calculator automatically converts degrees to radians for calculation.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the inputs provided, with results rounded to 6 decimal places for precision.