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Circumradius of Scalene Triangle Formula:
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The circumradius of a scalene triangle is the radius of the circumscribed circle that passes through all three vertices of the triangle. It represents the distance from the triangle's circumcenter to any of its vertices.
The calculator uses the formula:
Where:
Explanation: The formula relates the circumradius to the medium side and its opposite angle using trigonometric sine function.
Details: Calculating the circumradius is important in geometry for determining the size of the circumscribed circle, which has applications in various fields including engineering, architecture, and computer graphics.
Tips: Enter the medium side length in meters and the medium angle in degrees. The angle must be between 0° and 180° (exclusive), and the side length must be positive.
Q1: What is a scalene triangle?
A: A scalene triangle is a triangle with all three sides of different lengths and all three angles of different measures.
Q2: Why use the medium side and medium angle specifically?
A: The formula works with any side and its opposite angle. Using the medium side and medium angle provides consistent results regardless of which pair is chosen.
Q3: What are typical units for circumradius?
A: The circumradius is measured in the same units as the triangle's sides (meters, centimeters, inches, etc.).
Q4: Can this formula be used for other types of triangles?
A: Yes, this formula applies to all triangles, not just scalene triangles, as it's based on the extended law of sines.
Q5: What if I have the other sides and angles?
A: The formula can be adapted using any side and its opposite angle: \( r_c = \frac{a}{2\sin(A)} = \frac{b}{2\sin(B)} = \frac{c}{2\sin(C)} \)