Triangle calculator VC

Please enter the coordinates of the three vertices

Acute scalene triangle.

Sides: a = 3.60655512755   b = 4.12331056256   c = 3.16222776602

Area: T = 5.5
Perimeter: p = 10.89109345613
Semiperimeter: s = 5.44554672806

Angle ∠ A = α = 57.52988077092° = 57°31'44″ = 1.00440671093 rad
Angle ∠ B = β = 74.74548812969° = 74°44'42″ = 1.30545442776 rad
Angle ∠ C = γ = 47.72663109939° = 47°43'35″ = 0.83329812667 rad

Height: ha = 3.05108510792
Height: hb = 2.66878918754
Height: hc = 3.47985054262

Median: ma = 3.20215621187
Median: mb = 2.69325824036
Median: mc = 3.53655339059

Inradius: r = 1.01100143324
Circumradius: R = 2.13768471406

Vertex coordinates: A[1; 9] B[4; 8] C[2; 5]
Centroid: CG[2.33333333333; 7.33333333333]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[0.27554584543; 1.01100143324]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 122.4711192291° = 122°28'16″ = 1.00440671093 rad
∠ B' = β' = 105.2555118703° = 105°15'18″ = 1.30545442776 rad
∠ C' = γ' = 132.2743689006° = 132°16'25″ = 0.83329812667 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     