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

The obtuse angle of a rhombus is the angle greater than 90 degrees. Given the inradius (radius of the inscribed circle) and the side length, this calculator determines the obtuse angle using a specific trigonometric relationship.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \pi \) — Archimedes' constant (approximately 3.14159)
• \( \arcsin \) — Inverse sine function
• Inradius — Radius of the inscribed circle in the rhombus (m)
• Side — Length of any side of the rhombus (m)

Explanation: The formula derives from the geometric relationship between the inradius, side length, and the angles of the rhombus.

3. Importance of Obtuse Angle Calculation

Details: Calculating the obtuse angle is essential in geometry for understanding the properties of a rhombus, such as area, perimeter, and symmetry. It is also useful in various practical applications like design and architecture.

4. Using the Calculator

Tips: Enter the inradius and side length in meters. Both values must be positive, and the inradius must be less than or equal to half the side length for a valid rhombus.

5. Frequently Asked Questions (FAQ)

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

Q2: Why is the obtuse angle important?
A: The obtuse angle helps determine other properties of the rhombus, such as the area and the lengths of the diagonals.

Q3: Can the inradius be greater than half the side?
A: No, for a rhombus, the inradius cannot exceed half the side length; otherwise, the circle would not fit inside.

Q4: What units should I use?
A: The calculator uses meters, but any consistent unit can be used as long as both inputs are in the same unit.

Q5: Is the result in degrees or radians?
A: The result is displayed in degrees for ease of understanding, though the calculation is done in radians.