1. What is the Acute Angle of Rhombus given Inradius?

The acute angle of a rhombus given its inradius is calculated using the relationship between the inradius and the side length of the rhombus. This formula helps determine the smaller interior angle when the inscribed circle's radius is known.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• Inradius — Radius of the inscribed circle (m)
• Side — Length of any side of the rhombus (m)

Explanation: The formula derives from the geometric relationship between the inradius and the angles of a rhombus, using inverse sine function to find the acute angle.

3. Importance of Acute Angle Calculation

Details: Calculating the acute angle is essential for understanding the geometric properties of a rhombus, designing structures, and solving problems in various fields including engineering and architecture.

4. Using the Calculator

Tips: Enter the inradius and side length in meters. Both values must be positive numbers. The calculator will compute the acute angle in degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of valid inputs?
A: Both inradius and side must be positive numbers. The ratio (2*inradius/side) must be between -1 and 1 for valid results.

Q2: What units should I use?
A: The calculator uses meters for both inputs, but any consistent unit can be used as long as both measurements are in the same unit.

Q3: Can this formula be used for all rhombuses?
A: Yes, this formula applies to all rhombuses where an incircle exists and the relationship between inradius and side length is maintained.

Q4: What if I get an error message?
A: An error indicates that the calculated ratio falls outside the valid range for the inverse sine function. Check your input values.

Q5: How accurate is the calculation?
A: The calculation provides results accurate to four decimal places when valid inputs are provided.