Triangle calculator VC

Please enter the coordinates of the three vertices

Acute scalene triangle.

Sides: a = 15.52441746963   b = 15.62204993518   c = 16.76330546142

Area: T = 110
Perimeter: p = 47.90877286623
Semiperimeter: s = 23.95438643312

Angle ∠ A = α = 57.16595957285° = 57°9'35″ = 0.99876231446 rad
Angle ∠ B = β = 57.71545581856° = 57°42'52″ = 1.00773090667 rad
Angle ∠ C = γ = 65.12658460859° = 65°7'33″ = 1.13766604423 rad

Height: ha = 14.17114457808
Height: hb = 14.08440567926
Height: hc = 13.1244099698

Median: ma = 14.22114626533
Median: mb = 14.14221356237
Median: mc = 13.12444047484

Inradius: r = 4.5922160934
Circumradius: R = 9.23985522192

Vertex coordinates: A[3; -6] B[8; 10] C[-7; 6]
Centroid: CG[1.33333333333; 3.33333333333]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[2.90114107719; 4.5922160934]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 122.8440404271° = 122°50'25″ = 0.99876231446 rad
∠ B' = β' = 122.2855441814° = 122°17'8″ = 1.00773090667 rad
∠ C' = γ' = 114.8744153914° = 114°52'27″ = 1.13766604423 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     