ClarityHow to use this tool
- Enter the two known side lengths in metres.
- Enter the angle between those two sides in degrees, strictly between 0 and 180.
- Calculate the opposite side, triangle area and perimeter.
Input reference and sample values
Use the units and choices shown for each field. Sample values are provided for practice, not as recommendations.
| Input | Format and units | Sample |
|---|---|---|
| First side | Numeric value. Unit: m. Must be greater than zero. | 3 |
| Second side | Numeric value. Unit: m. Must be greater than zero. | 4 |
| Included angle | Numeric value. Unit: degrees. Minimum: 0.000001. Maximum: 179.999999. | 90 |
Result for these sample inputs
5 m
- Included angle (degrees)
- 90
- Triangle area (m²)
- 6
- Perimeter (m)
- 12
Select Try the example in the form to load these values and calculate them again. This replaces the current form inputs. Compare the result with the method and worked explanation below.
The method, explained
c = √[(a − b)² + 4ab sin²(C/2)], equivalent to c² = a² + b² − 2ab cos C. The half-angle form avoids subtracting nearly equal terms for small angles.
Sides 3 m and 4 m enclosing 90° give the opposite side 5 m, area 6 m² and perimeter 12 m.
What to keep in mind
This is the side-angle-side case; the angle must lie between the entered sides. It does not solve a triangle from three sides or from a non-included angle. Very small angles remain sensitive to measurement precision.
Common questions
Is the angle entered in radians?
No. Enter degrees; a right angle is 90.
Can the answer be zero for two equal sides?
Not for a positive included angle. The stable half-angle calculation preserves a small positive third side.
Methodology maintained by ClarityKit. How these tools are built and checked.