Circumference of Circumcircle of Scalene Triangle Calculator

Circumference of Circumcircle Formula:

\[ C_{Circumcircle} = \pi \times \frac{S_{Shorter}}{\sin(\angle_{Smaller})} \]

Circumference of Circumcircle:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Circumference of Circumcircle of Scalene Triangle?

The circumference of the circumcircle of a scalene triangle is the total distance around the circle that passes through all three vertices of the triangle. It provides important geometric information about the triangle's circumscribed circle.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ C_{Circumcircle} = \pi \times \frac{S_{Shorter}}{\sin(\angle_{Smaller})} \]

Where:

\( C_{Circumcircle} \) — Circumference of circumcircle (m)
\( \pi \) — Mathematical constant pi (≈3.14159)
\( S_{Shorter} \) — Shorter side of scalene triangle (m)
\( \angle_{Smaller} \) — Smaller angle of scalene triangle (degrees)
\( \sin \) — Sine trigonometric function

Explanation: This formula calculates the circumference of the circle that circumscribes the scalene triangle using the shorter side and the angle opposite to it.

3. Importance of Circumcircle Calculation

Details: Calculating the circumcircle circumference is important in geometry, engineering, and design applications where circular properties of triangular shapes need to be determined.

4. Using the Calculator

Tips: Enter the length of the shorter side in meters and the smaller angle in degrees. Both values must be positive, and the angle must be between 0 and 180 degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is a circumcircle?
A: A circumcircle is a circle that passes through all the vertices of a polygon. For a triangle, it's the unique circle that contains all three vertices.

Q2: Why use the shorter side and smaller angle?
A: The formula utilizes the relationship between a side length and its opposite angle through the sine function in the extended law of sines.

Q3: Can this formula be used for other types of triangles?
A: Yes, this formula works for all types of triangles (scalene, isosceles, equilateral) as it's based on the extended law of sines.

Q4: What are the units of measurement?
A: The side length should be in meters, and the result will be in meters. You can use any consistent unit system as long as you maintain consistency.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the input values. The accuracy depends on the precision of your input measurements.