1. What is the Triangle Side Length Formula?

The formula \( a = 2R \times \sin(A) \) calculates the length of a side of a triangle when you know the circumradius (R) and the angle opposite that side (A). This is particularly useful in circular geometry and trigonometric applications.

2. How Does the Calculator Work?

The calculator uses the triangle side length formula:

Where:

• \( a \) — Length of the side (same units as radius)
• \( R \) — Circumradius of the triangle
• \( A \) — Angle opposite side a (in degrees or radians)

Explanation: The formula relates a triangle's side length to its circumradius and the angle opposite that side through the sine function.

3. Importance of Side Length Calculation

Details: Calculating side lengths from angles and radius is essential in trigonometry, navigation, engineering, and physics problems involving circular motion or periodic phenomena.

4. Using the Calculator

Tips: Enter the radius in any length units, the angle value, and select 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 that passes through all three vertices of the triangle.

Q2: Can this formula be used for any triangle?
A: Yes, this formula works for all triangles as long as you know the circumradius and the angle opposite the side you're calculating.

Q3: What's the difference between degrees and radians?
A: Degrees and radians are two units for measuring angles. 360° = 2π radians. The calculator handles both.

Q4: What if my angle is greater than 180 degrees?
A: The formula still works mathematically, but such angles don't correspond to standard triangle geometry.

Q5: How precise are the results?
A: Results are precise to 4 decimal places, but actual precision depends on your input measurements.