1. What is the Law of Sines?

The Law of Sines is a trigonometric equation relating the lengths of sides of a triangle to the sines of its opposite angles. It's particularly useful for solving triangles when you know either two angles and one side (AAS or ASA) or two sides and a non-included angle (SSA).

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( a \) — Length of the side opposite angle A
• \( r \) — Radius of the circumscribed circle
• \( A \) — Angle opposite side a (in degrees or radians)

Explanation: This formula calculates the length of a side of a triangle given the radius of its circumscribed circle and the angle opposite that side.

3. Importance of Triangle Side Calculation

Details: Calculating triangle sides is fundamental in geometry, engineering, architecture, and navigation. It helps in determining unknown dimensions when partial information is available.

4. Using the Calculator

Tips: Enter the radius in any length units, the angle value, and specify whether the angle is in degrees or radians. The result will be in the same units as the radius.

5. Frequently Asked Questions (FAQ)

Q1: What is the circumradius of a triangle?
A: The radius of the circumscribed circle (circumcircle) that passes through all three vertices of the triangle.

Q2: Can I use this for any triangle?
A: Yes, the Law of Sines applies to all triangles, whether acute, right, or obtuse.

Q3: What if I know two sides and an angle?
A: You can use the Law of Sines to find other angles, but be aware of the ambiguous case (SSA) where two solutions might exist.

Q4: How precise are the results?
A: Results are precise to 4 decimal places, but actual precision depends on the precision of your inputs.

Q5: Can I use this for 3D triangles?
A: This calculator is for 2D triangles. For 3D applications, you would need additional trigonometric calculations.