Area Of Triangle Using Sine Calculator

Work out area of triangle using sine instantly with clear inputs, formula shown and shareable results.

About Area Of Triangle Using Sine Calculator

When two sides and the angle between them are known, the area is ½ab·sin C. The perpendicular height onto side a is b·sin C, which is exactly what turns the familiar ½ × base × height into this form.

Formulas

Area (SAS)

Area = ½ · a · b · sin C

Law of cosines

c² = a² + b² − 2ab·cos C

Worked example

With the default values below, Area Of Triangle Using Sine Calculator returns Area of 20.0000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Side aminimum 0: 8
Side bminimum 0: 10
Included angle Caccepts 0–180 °: 30 °

Results

Area: 20.0000
Third side c (law of cosines): 5.0434
Perimeter: 23.0434
sin C: 0.50000000

Step by step

1Values used
2Area (SAS)
3Law of cosines
4Area= 20.0000
5Third side c (law of cosines)= 5.0434
6Perimeter= 23.0434
7sin C= 0.50000000

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

a = 8, b = 10, C = 30°?

½ × 8 × 10 × 0.5 = 20 square units, since sin 30° = 0.5 exactly.

Does the angle have to be between the two sides?

Yes. Using a non-included angle gives the wrong area; for that case solve the triangle first.