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Oblique Triangle Area Calculator — result sheet
Calculate the area, third side, and altitude of an oblique triangle from two sides and their included obtuse angle.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Area = ½ab sin(C); third side c = √(a²+b²−2ab cos(C)); altitude to side a = b sin(C).
An obtuse triangle still uses the sine area formula when the angle between the two entered sides is greater than 90 degrees. The calculator also derives the opposite side with the law of cosines and shows the corresponding altitude so the geometry is auditable.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- First side — length units; minimum 1.0E-6; maximum 1000000000
- Second side — length units; minimum 1.0E-6; maximum 1000000000
- Included angle — degrees; minimum 90.000001; maximum 179.999999
Worked example
| Input | Value |
|---|---|
| First side | 5 |
| Second side | 7 |
| Included angle | 120 |
Area ≈15.1554 square units; third side ≈10.4403 units; altitude to side a ≈6.0622 units.
Assumptions and limits
- The two side inputs are positive and use one consistent length unit.
- The included angle is strictly obtuse and is entered in degrees.
- The triangle is planar and Euclidean.
- The included angle is the angle between the two entered sides, not an exterior angle.
- The altitude is measured perpendicular to side a and can land outside the segment when the angle is obtuse.
- The result is a geometric calculation, not a survey adjustment or construction tolerance.
- Rounding is applied only for display; the underlying handler retains the numeric result.
- Use measured angles and sides with their uncertainty when this is part of a physical layout.
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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