Calculate Sas Triangle

SAS Triangle Formulas:

\[ c² = a² + b² - 2ab \cos(C) \] \[ A = \arccos\left(\frac{b² + c² - a²}{2bc}\right) \] \[ B = \arccos\left(\frac{a² + c² - b²}{2ac}\right) \]

Side c:

Angle A:

Angle B:

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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 based on the Law of Cosines and Law of Sines in trigonometry.

2. How Does the Calculator Work?

The calculator uses these formulas:

\[ c² = a² + b² - 2ab \cos(C) \] \[ A = \arccos\left(\frac{b² + c² - a²}{2bc}\right) \] \[ B = \arccos\left(\frac{a² + c² - b²}{2ac}\right) \]

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 respectively

Explanation: The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles.

3. Importance of Triangle Calculations

Details: SAS triangle calculations are fundamental in geometry, navigation, engineering, and physics for solving real-world problems involving triangular relationships.

4. Using the Calculator

Tips: Enter two side lengths and the included angle in degrees. All values must be positive, and the angle must be between 0 and 180 degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is the SAS condition?
A: SAS (Side-Angle-Side) is a congruence rule stating that if two sides and the included angle of one triangle are equal to those of another, the triangles are congruent.

Q2: How accurate are the results?
A: Results are mathematically precise, though displayed with 2 decimal places for readability. Extreme values may have floating-point precision limitations.

Q3: Can I use this for any triangle?
A: Yes, as long as you have two sides and the included angle. For other combinations (SSS, ASA, etc.), different methods are needed.

Q4: What units should I use?
A: Any consistent length units (cm, m, inches, etc.). Angles must be in degrees (0-180).

Q5: What if I get an error?
A: Check that all inputs are positive numbers, the angle is between 0 and 180 degrees, and the sides form a valid triangle (sum of any two sides > third side).