1. What is the Side of Rhombus given Inradius Formula?

The formula calculates the side length of a rhombus when given its inradius and acute angle. It demonstrates the relationship between the inscribed circle and the geometry of the rhombus.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( S \) — Side of Rhombus (m)
• \( r_i \) — Inradius of Rhombus (m)
• \( \angle Acute \) — Acute Angle of Rhombus (degrees)

Explanation: The formula derives from the trigonometric relationship between the inradius, side length, and the acute angle of the rhombus.

3. Importance of Side Length Calculation

Details: Calculating the side length of a rhombus is essential in geometry problems, architectural design, and various engineering applications where rhombus-shaped structures are used.

4. Using the Calculator

Tips: Enter the inradius in meters and the acute angle in degrees. Both values must be positive, and the angle must be between 0 and 90 degrees.

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: Why does the formula use the sine function?
A: The sine function relates the acute angle to the ratio between the inradius and side length through the geometry of the rhombus.

Q4: Can this formula be used for obtuse angles?
A: No, this specific formula uses the acute angle. For obtuse angles, a different trigonometric relationship would apply.

Q5: What are practical applications of this calculation?
A: This calculation is useful in various fields including architecture, engineering design, and geometric problem solving involving rhombus shapes.