Triangle calculator VC

Please enter the coordinates of the three vertices

Acute scalene triangle.

Sides: a = 12.64991106407   b = 15.29770585408   c = 14.21326704036

Area: T = 84
Perimeter: p = 42.1598839585
Semiperimeter: s = 21.07994197925

Angle ∠ A = α = 50.59993393365° = 50°35'58″ = 0.88331250708 rad
Angle ∠ B = β = 69.14655419604° = 69°8'44″ = 1.20768173703 rad
Angle ∠ C = γ = 60.25551187031° = 60°15'18″ = 1.05216502125 rad

Height: ha = 13.28215661727
Height: hb = 10.98325035677
Height: hc = 11.82204387515

Median: ma = 13.34216640641
Median: mb = 11.06879718106
Median: mc = 12.10437184369

Inradius: r = 3.98549294158
Circumradius: R = 8.18547294346

Vertex coordinates: A[0; 6] B[-9; -5] C[3; -9]
Centroid: CG[-2; -2.66766666667]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[1.51880683489; 3.98549294158]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 129.4010660663° = 129°24'2″ = 0.88331250708 rad
∠ B' = β' = 110.854445804° = 110°51'16″ = 1.20768173703 rad
∠ C' = γ' = 119.7454881297° = 119°44'42″ = 1.05216502125 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     