Law of Cosines
Find the missing side and area from two sides and their included angle.
Your numbers
Opposite side
Use consistent units. The result follows the assumptions you enter.
Scenario comparison
Up to three snapshots in this tab. Loading one replaces the current inputs.
Formula
Use a² = b²+c²−2bc cos(A) and K = bc sin(A)/2. b and c are the entered sides and A is their included angle in degrees. a is the opposite side and K is triangle area.
Find the missing side and area from two sides and their included angle.
Worked example
- First side (m)
- 3
- Second side (m)
- 4
- Included angle (degrees)
- 90
- Opposite side
- 5 m
- Area
- 6 m²
Scope and limitations
Use consistent units. The result follows the assumptions you enter.
Inputs are checked for missing values and allowed ranges. A result outside the finite numeric range is not displayed. Rounding affects display, while the calculation uses the model’s numeric precision.
Check your units and assumptions before relying on a result. Changing a label does not convert a currency or physical unit.
Formula version: 560181d3f568 · Example checked: