Triangle calculator VC

Please enter the coordinates of the three vertices

Acute scalene triangle.

Sides: a = 3.60655512755   b = 7.07110678119   c = 6.40331242374

Area: T = 11.5
Perimeter: p = 17.08797433248
Semiperimeter: s = 8.54398716624

Angle ∠ A = α = 30.53297058999° = 30°31'47″ = 0.53328438876 rad
Angle ∠ B = β = 85.03302592719° = 85°1'49″ = 1.48440579881 rad
Angle ∠ C = γ = 64.44400348282° = 64°26'24″ = 1.12546907779 rad

Height: ha = 6.37990522566
Height: hb = 3.25326911935
Height: hc = 3.59219965234

Median: ma = 6.5
Median: mb = 3.80878865529
Median: mc = 4.61097722286

Inradius: r = 1.34766244523
Circumradius: R = 3.54988755907

Vertex coordinates: A[0; 0] B[4; 5] C[1; 7]
Centroid: CG[1.66766666667; 4]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[0.11770977785; 1.34766244523]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.47702941° = 149°28'13″ = 0.53328438876 rad
∠ B' = β' = 94.97697407281° = 94°58'11″ = 1.48440579881 rad
∠ C' = γ' = 115.5659965172° = 115°33'36″ = 1.12546907779 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     