Triangle calculator VC

Please enter the coordinates of the three vertices

Acute scalene triangle.

Sides: a = 4.24326406871   b = 6.40331242374   c = 7.28801098893

Area: T = 13.5
Perimeter: p = 17.92658748138
Semiperimeter: s = 8.96329374069

Angle ∠ A = α = 35.3954795845° = 35°23'41″ = 0.61877557256 rad
Angle ∠ B = β = 60.94553959009° = 60°56'43″ = 1.06436978224 rad
Angle ∠ C = γ = 83.66598082541° = 83°39'35″ = 1.46601391056 rad

Height: ha = 6.36439610307
Height: hb = 4.2176691571
Height: hc = 3.70987352266

Median: ma = 6.51992024052
Median: mb = 5.02549378106
Median: mc = 4.03111288741

Inradius: r = 1.50662026417
Circumradius: R = 3.66224554942

Vertex coordinates: A[0; 5] B[2; -2] C[5; 1]
Centroid: CG[2.33333333333; 1.33333333333]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[0.83767792454; 1.50662026417]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.6055204155° = 144°36'19″ = 0.61877557256 rad
∠ B' = β' = 119.0554604099° = 119°3'17″ = 1.06436978224 rad
∠ C' = γ' = 96.34401917459° = 96°20'25″ = 1.46601391056 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     