Triangle calculator VC

Please enter the coordinates of the three vertices

Acute scalene triangle.

Sides: a = 11.4021754251   b = 9.43439811321   c = 7.81102496759

Area: T = 36.5
Perimeter: p = 28.6465985059
Semiperimeter: s = 14.32329925295

Angle ∠ A = α = 82.21998121158° = 82°11'59″ = 1.43546573659 rad
Angle ∠ B = β = 55.06106897953° = 55°3'38″ = 0.96109903253 rad
Angle ∠ C = γ = 42.73994980889° = 42°44'22″ = 0.74659449623 rad

Height: ha = 6.40325235409
Height: hb = 7.7387984524
Height: hc = 9.34766922351

Median: ma = 6.51992024052
Median: mb = 8.55986213843
Median: mc = 9.70882439195

Inradius: r = 2.54883501388
Circumradius: R = 5.75441177012

Vertex coordinates: A[4; 0] B[-1; 6] C[-4; -5]
Centroid: CG[-0.33333333333; 0.33333333333]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[1.78803542065; 2.54883501388]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 97.88001878842° = 97°48'1″ = 1.43546573659 rad
∠ B' = β' = 124.9399310205° = 124°56'22″ = 0.96109903253 rad
∠ C' = γ' = 137.2610501911° = 137°15'38″ = 0.74659449623 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     