Scalene Triangle Solver (Area, Angles and Radii)

Enter three sides, or two sides with the included angle, to compute area (Heron formula), perimeter, all three angles, every height, the inradius and circumradius, and the centroid. The triangle inequality is checked automatically.

Input

Enter three sides, or two sides with the included angle, to compute area, perimeter, angles, heights, the inradius and circumradius, and the centroid.

Input method

Side a length

Side b length

Side c length

Result

Area

26.832816

Area

26.832816

Perimeter

Angle A

48.189685 deg

Angle B

58.411864 deg

Angle C

73.39845 deg

Height onto a

7.666519

Height onto b

6.708204

Height onto c

5.962848

Inradius

2.236068

Circumradius

4.695743

Lengths share the unit of the input values, area is in that unit squared, and angles are shown in degrees.

How it works

For the three sides mode (SSS), the triangle inequality (the sum of any two sides is greater than the third) is checked first and an error is shown if it fails.
Area uses the Heron formula S=sqrt(s(s-a)(s-b)(s-c)), where s is the semi perimeter.
Each angle comes from the law of cosines, for example cosA=(b squared + c squared - a squared) divided by 2bc, and is reported in both degrees and radians.
The height onto each side equals 2S divided by that side length.
The inradius is r=S divided by s, and the circumradius is R=abc divided by 4S.
For the two sides and included angle mode (SAS), the remaining side is found with the law of cosines and then the same steps are applied.
The centroid is the average of the three vertex coordinates, and the diagram shows the medians from each vertex as dotted lines.
Lengths share the unit of the input values, and area is in that unit squared.

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