Triangle calculator VC

Please enter the coordinates of the three vertices

Acute scalene triangle.

Sides: a = 9.84988578018   b = 10.81766538264   c = 5.83109518948

Area: T = 28.5
Perimeter: p = 26.4966463523
Semiperimeter: s = 13.24882317615

Angle ∠ A = α = 64.65438240581° = 64°39'14″ = 1.12884221038 rad
Angle ∠ B = β = 82.99987324425° = 82°59'55″ = 1.44986011561 rad
Angle ∠ C = γ = 32.34774434994° = 32°20'51″ = 0.56545693937 rad

Height: ha = 5.78774731413
Height: hb = 5.27696518641
Height: hc = 9.77554193531

Median: ma = 7.15989105316
Median: mb = 6.02107972894
Median: mc = 9.92547166206

Inradius: r = 2.15112304822
Circumradius: R = 5.44989573071

Vertex coordinates: A[5; 4] B[0; 7] C[-4; -2]
Centroid: CG[0.33333333333; 3]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[0.26441861996; 2.15112304822]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 115.3466175942° = 115°20'46″ = 1.12884221038 rad
∠ B' = β' = 97.00112675575° = 97°5″ = 1.44986011561 rad
∠ C' = γ' = 147.6532556501° = 147°39'9″ = 0.56545693937 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     