Triangle calculator VC

Please enter the coordinates of the three vertices

Acute scalene triangle.

Sides: a = 15.23215462117   b = 16.49224225025   c = 14.14221356237

Area: T = 100
Perimeter: p = 45.86661043379
Semiperimeter: s = 22.9333052169

Angle ∠ A = α = 59.03662434679° = 59°2'10″ = 1.03303768265 rad
Angle ∠ B = β = 68.19985905136° = 68°11'55″ = 1.19902899497 rad
Angle ∠ C = γ = 52.76551660184° = 52°45'55″ = 0.92109258774 rad

Height: ha = 13.1310643286
Height: hb = 12.12767812518
Height: hc = 14.14221356237

Median: ma = 13.34216640641
Median: mb = 12.16655250606
Median: mc = 14.21326704036

Inradius: r = 4.36105185766
Circumradius: R = 8.88114413245

Vertex coordinates: A[-6; -4] B[4; 6] C[10; -8]
Centroid: CG[2.66766666667; -2]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[1.74442074306; 4.36105185766]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 120.9643756532° = 120°57'50″ = 1.03303768265 rad
∠ B' = β' = 111.8011409486° = 111°48'5″ = 1.19902899497 rad
∠ C' = γ' = 127.2354833982° = 127°14'5″ = 0.92109258774 rad

How did we calculate this triangle?

1. We compute side a from coordinates using the Pythagorean theorem 2. We compute side b from coordinates using the Pythagorean theorem 3. We compute side c from coordinates using the Pythagorean theorem Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS. 4. The triangle circumference is the sum of the lengths of its three sides 5. Semiperimeter of the triangle 6. The triangle area using Heron's formula 7. Calculate the heights of the triangle from its area. 8. Calculation of the inner angles of the triangle using a Law of Cosines     