Triangle Area from Two Sides and Included Angle

Find the area of a triangle from two side lengths and their included angle using (1/2)ab sin C. Also shows the opposite side and perimeter.

Input

Enter two side lengths and the angle between them to compute the area with (1/2)ab sin C.

Side a

Side b

Angle unit

Included angle C

Area S

20.78461

Side a

Side b

Included angle C

60 deg (1.047198 rad)

Opposite side c

7.211103

Perimeter

21.211103

Lengths share the input unit, and the area is in that unit squared.

The area is computed as S = (1/2)ab sin C, where a and b are two side lengths and C is the angle between them (the included angle).
You can enter the angle in degrees or radians. The calculator converts to radians internally before computing.
The side c opposite the included angle is found with the law of cosines: c = sqrt(a squared plus b squared minus 2ab cos C).
For a valid triangle the included angle C must be greater than 0 degrees and less than 180 degrees.
Lengths use the same unit as the inputs, and the area is expressed in that unit squared.

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