1. What is the Triangle Side Formula?

The formula \( a = \frac{c \times \sin A}{\sin C} \) is derived from the Law of Sines and allows calculation of an unknown side of a triangle when you know one side and two angles.

2. How Does the Calculator Work?

The calculator uses the triangle side formula:

Where:

• \( a \) — The side we want to calculate
• \( c \) — The known side length
• \( A \) — Angle opposite side a
• \( C \) — Angle opposite side c

Explanation: The formula comes from the Law of Sines which states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides and angles in a triangle.

3. Importance of Triangle Side Calculation

Details: Calculating unknown sides of triangles is fundamental in geometry, trigonometry, navigation, architecture, and many engineering applications.

4. Using the Calculator

Tips: Enter known side length in meters, known angles in degrees. All values must be positive (side > 0, angles between 0-180 degrees).

5. Frequently Asked Questions (FAQ)

Q1: What if I know two sides and one angle?
A: Use the Law of Cosines to find the remaining sides and angles.

Q2: Does this work for all types of triangles?
A: Yes, the Law of Sines applies to all triangles, whether acute, right, or obtuse.

Q3: What units should I use?
A: The calculator uses meters for length and degrees for angles, but any consistent units will work.

Q4: What if my angles add up to more than 180 degrees?
A: The calculator will still compute a result, but it won't represent a valid Euclidean triangle.

Q5: Can I calculate angles with this formula?
A: The formula is for side calculation. To find angles, you would rearrange the Law of Sines.