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SAS Triangle Area Calculator — result sheet
Calculate the area and opposite side of a triangle from two sides and their included angle.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Area = 1/2 ab sin(C); opposite side c = √(a²+b²−2ab cos(C)).
The included angle identifies the two sides that bound the area and determines the third side through the cosine rule.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Side A — length; minimum 1.0E-6; maximum 1000000
- Side B — length; minimum 1.0E-6; maximum 1000000
- Included angle — degrees; minimum 1.0E-6; maximum 179.999999
Worked example
| Input | Value |
|---|---|
| Side A | 5 |
| Side B | 7 |
| Included angle | 40 |
Area ≈ 11.249 square units; opposite side ≈ 4.514 units.
Assumptions and limits
- The two sides are positive and the included angle is strictly between 0 and 180 degrees.
- The triangle is Euclidean and all length inputs use one consistent unit.
- Rounding, measurement uncertainty, and surveying tolerances are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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