1. What is the Obtuse Angle of Tri-equilateral Trapezoid?

The Obtuse Angle of Tri-equilateral Trapezoid is any of the angles on the shorter base or the shorter edge among the parallel edges of the Tri-equilateral Trapezoid. It is calculated as the difference between π (pi) and the acute angle.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \pi \) — Archimedes' constant (approximately 3.14159)
• Acute Angle — Acute angle of the tri-equilateral trapezoid in radians

Explanation: In a tri-equilateral trapezoid, the sum of adjacent angles along the same side is π radians (180 degrees). Therefore, the obtuse angle can be found by subtracting the acute angle from π.

3. Importance of Angle Calculation

Details: Accurate angle calculation is crucial for geometric analysis, construction planning, and understanding the properties of tri-equilateral trapezoids in various applications.

4. Using the Calculator

Tips: Enter the acute angle value in radians (0 to π). The calculator will compute the corresponding obtuse angle using the formula π - acute angle.

5. Frequently Asked Questions (FAQ)

Q1: What is a tri-equilateral trapezoid?
A: A tri-equilateral trapezoid is a trapezoid with three equal sides, creating specific angle relationships between the bases.

Q2: Why is π used in the formula?
A: π radians equals 180 degrees, which is the total angle measure on one side of a straight line in Euclidean geometry.

Q3: What are the valid input ranges?
A: The acute angle must be between 0 and π radians (0° to 180°). The resulting obtuse angle will also be between 0 and π radians.

Q4: Can I use degrees instead of radians?
A: This calculator requires input in radians. To convert from degrees to radians, multiply degrees by π/180.

Q5: What are typical applications of this calculation?
A: This calculation is used in geometry problems, architectural design, engineering applications, and various mathematical analyses involving trapezoidal shapes.