Solve Sas Triangle Calculator

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?

A SAS (Side-Angle-Side) triangle is one where we know two sides and the included angle. This calculator solves for the remaining side and angles using trigonometric formulas.

2. How Does the Calculator Work?

The calculator uses the Law of Cosines and Law of Sines:

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

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

3. Importance of Triangle Solving

Details: Solving triangles is fundamental in geometry, physics, engineering, and navigation. SAS is one of the most common triangle configurations encountered in real-world problems.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What units should I use?
A: Any consistent length units (cm, m, inches, etc.). Angle must be in degrees.

Q2: What if my angle is in radians?
A: Convert to degrees first (1 radian ≈ 57.2958 degrees).

Q3: Can I use this for right triangles?
A: Yes, but simpler right triangle formulas would also work when one angle is 90°.

Q4: What if I get NaN or unexpected results?
A: Check your inputs form a valid triangle (sum of two sides > third side, angles sum to 180°).

Q5: How accurate are the results?
A: Results are accurate to floating-point precision, displayed with 2 decimal places.