Triangle calculator VC

Please enter the coordinates of the three vertices

Acute scalene triangle.

Sides: a = 8.24662112512   b = 8.6022325267   c = 7.07110678119

Area: T = 27
Perimeter: p = 23.92196043301
Semiperimeter: s = 11.96598021651

Angle ∠ A = α = 62.59224245622° = 62°35'33″ = 1.09224438954 rad
Angle ∠ B = β = 67.83436541779° = 67°50'1″ = 1.18439206091 rad
Angle ∠ C = γ = 49.57439212599° = 49°34'26″ = 0.86552281491 rad

Height: ha = 6.5488461876
Height: hb = 6.27773724922
Height: hc = 7.63767532368

Median: ma = 6.70882039325
Median: mb = 6.36439610307
Median: mc = 7.64985292704

Inradius: r = 2.25875624268
Circumradius: R = 4.64444208163

Vertex coordinates: A[3; 4] B[4; -3] C[-4; -1]
Centroid: CG[1; 0]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[0.92197476554; 2.25875624268]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 117.4087575438° = 117°24'27″ = 1.09224438954 rad
∠ B' = β' = 112.1666345822° = 112°9'59″ = 1.18439206091 rad
∠ C' = γ' = 130.426607874° = 130°25'34″ = 0.86552281491 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     