Free · Triangle calculators 🔺

Triangle Sides and Area from Opposite Side and Two Angles

The height is perpendicular to side b, so area is b times that height divided by two. Side a lies opposite α; enter a, α and β. The remaining measures are read-only outputs.

Formula & worked example
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How to use this calculator

Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

Example in initial displayed units: a 4, Angle α 90, Angle β 30 gives b 2, c 3.464102, Angle γ 60, Height perpendicular to side b 3.464102, Area 3.464102.

b/a = sin β/sin α; γ = π−α−β; area = ab sin γ/2

Worked example

Enter these known values and leave the other values blank.

a: 4 cm
Angle α: 90 deg
Angle β: 30 deg

b: 2 cm
c: 3.464 cm
Angle γ: 60 deg
Height perpendicular to side b: 3.464 cm
Area: 3.464 cm²

Assumptions and limitations

Side a is opposite α; b and c are opposite β and γ. Enter a and two angles. The height shown is perpendicular to side b. All remaining measures are one-way, read-only results. Positive angles must sum to less than π.
Use compatible units and enough independent values. Clear unknowns before solving backward. Original reference drawings are schematic and do not scale to entered values.

Common questions

Which side is the reported triangle height perpendicular to?