Sas Triangle Calculator

SAS Triangle Formula:

\[ side_c = \sqrt{a^2 + b^2 - 2 \times a \times b \times \cos(c)} \]

Side c:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the SAS Triangle Formula?

The SAS (Side-Angle-Side) formula calculates the length of the third side of a triangle when two sides and the included angle are known. It's derived from the Law of Cosines and is essential in trigonometry and geometry.

2. How Does the Calculator Work?

The calculator uses the SAS formula:

\[ side_c = \sqrt{a^2 + b^2 - 2 \times a \times b \times \cos(c)} \]

Where:

\( a \) — Length of side a (units)
\( b \) — Length of side b (units)
\( c \) — Included angle in radians

Explanation: The formula accounts for the relationship between two sides and their included angle to determine the third side of a triangle.

3. Importance of SAS Calculation

Details: SAS calculations are crucial in trigonometry, navigation, engineering, and physics where triangle measurements are needed but not all sides are directly measurable.

4. Using the Calculator

Tips: Enter side lengths in any consistent units, and the included angle in radians. All values must be positive (angle between 0-π radians).

5. Frequently Asked Questions (FAQ)

Q1: Can I use degrees instead of radians?
A: This calculator uses radians. Convert degrees to radians by multiplying by π/180.

Q2: What if I know two angles and one side?
A: Use the Law of Sines instead for ASA (Angle-Side-Angle) cases.

Q3: Does this work for any triangle?
A: Yes, the SAS formula works for all triangles - acute, right, or obtuse.

Q4: What's the maximum angle allowed?
A: The angle must be less than π radians (180 degrees) to form a valid triangle.

Q5: How accurate are the results?
A: Results are accurate to 4 decimal places, assuming precise input values.