1. What is SAS Triangle Calculation?

The SAS (Side-Angle-Side) triangle calculation determines the unknown sides and angles of a triangle when two sides and the included angle are known. This is done using the Law of Cosines and Law of Sines.

2. How Does the Calculator Work?

The calculator uses the following formulas:

Where:

• \( a, b \) — Known sides
• \( C \) — Included angle between sides a and b
• \( c \) — Calculated side opposite angle C
• \( A, B \) — Calculated angles opposite sides a and b

Explanation: The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles, allowing calculation of the third side when two sides and the included angle are known.

3. Importance of SAS Calculation

Details: SAS calculations are fundamental in trigonometry and have applications in navigation, engineering, physics, and computer graphics where triangular relationships need to be determined.

4. Using the Calculator

Tips: Enter the lengths of two sides and the included angle in degrees. All values must be positive numbers (side lengths > 0, angle between 0-180 degrees).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between SAS and SSS?
A: SAS means you know two sides and the included angle, while SSS means you know all three sides but none of the angles.

Q2: Can this calculator handle obtuse angles?
A: Yes, the calculator works for all angles between 0° and 180°.

Q3: What units should I use?
A: Any consistent units can be used for side lengths (cm, m, inches, etc.). Angles must be in degrees.

Q4: Why do I sometimes get slightly different results from other calculators?
A: Small differences may occur due to rounding methods or floating-point precision in different implementations.

Q5: What if my triangle is right-angled?
A: The calculator still works, but you could also use the simpler Pythagorean theorem for right-angled triangles.