Triangle calculator VC

Please enter the coordinates of the three vertices

Acute scalene triangle.

Sides: a = 12.36993168769   b = 8.06222577483   c = 12.08330459736

Area: T = 46.5
Perimeter: p = 32.51546205987
Semiperimeter: s = 16.25773102994

Angle ∠ A = α = 72.68110615685° = 72°40'52″ = 1.26985238282 rad
Angle ∠ B = β = 38.48801982483° = 38°28'49″ = 0.67216061563 rad
Angle ∠ C = γ = 68.83987401832° = 68°50'19″ = 1.20114626691 rad

Height: ha = 7.51986043761
Height: hb = 11.53552303168
Height: hc = 7.6976734764

Median: ma = 8.20106097334
Median: mb = 11.54333963806
Median: mc = 8.5154693183

Inradius: r = 2.86602517356
Circumradius: R = 6.47883719258

Vertex coordinates: A[0; -2] B[-5; 9] C[-8; -3]
Centroid: CG[-4.33333333333; 1.33333333333]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[3.59883812158; 2.86602517356]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 107.3198938432° = 107°19'8″ = 1.26985238282 rad
∠ B' = β' = 141.5219801752° = 141°31'11″ = 0.67216061563 rad
∠ C' = γ' = 111.1611259817° = 111°9'41″ = 1.20114626691 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     