Triangle calculator VC

Please enter the coordinates of the three vertices

Acute scalene triangle.

Sides: a = 7.07110678119   b = 6.08327625303   c = 7.81102496759

Area: T = 20.5
Perimeter: p = 20.96440800181
Semiperimeter: s = 10.4822040009

Angle ∠ A = α = 59.65767511158° = 59°39'24″ = 1.0411206728 rad
Angle ∠ B = β = 47.93656734464° = 47°56'8″ = 0.83766353308 rad
Angle ∠ C = γ = 72.40875754378° = 72°24'27″ = 1.26437505948 rad

Height: ha = 5.79882756057
Height: hb = 6.74403584795
Height: hc = 5.25495120772

Median: ma = 6.04215229868
Median: mb = 6.80107352544
Median: mc = 5.31550729064

Inradius: r = 1.95657261738
Circumradius: R = 4.09767261054

Vertex coordinates: A[7; 6] B[1; 1] C[8; 0]
Centroid: CG[5.33333333333; 2.33333333333]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[1.76549236202; 1.95657261738]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 120.3433248884° = 120°20'36″ = 1.0411206728 rad
∠ B' = β' = 132.0644326554° = 132°3'52″ = 0.83766353308 rad
∠ C' = γ' = 107.5922424562° = 107°35'33″ = 1.26437505948 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     