Triangle calculator VC

Please enter the coordinates of the three vertices

Obtuse scalene triangle.

Sides: a = 16.49224225025   b = 24.16660919472   c = 15.23215462117

Area: T = 124
Perimeter: p = 55.89900606614
Semiperimeter: s = 27.94550303307

Angle ∠ A = α = 42.35774547059° = 42°21'27″ = 0.73992770474 rad
Angle ∠ B = β = 99.16223470457° = 99°9'44″ = 1.731070945 rad
Angle ∠ C = γ = 38.48801982483° = 38°28'49″ = 0.67216061563 rad

Height: ha = 15.03772087523
Height: hb = 10.26223130187
Height: hc = 16.28219976746

Median: ma = 18.43990889146
Median: mb = 10.2965630141
Median: mc = 19.23553840617

Inradius: r = 4.4377282713
Circumradius: R = 12.23992045065

Vertex coordinates: A[-11; -2; 0] B[-5; 12; 0] C[11; 8; 0]
Centroid: CG[-1.66766666667; 6; 0]
Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.6432545294° = 137°38'33″ = 0.73992770474 rad
∠ B' = β' = 80.83876529543° = 80°50'16″ = 1.731070945 rad
∠ C' = γ' = 141.5219801752° = 141°31'11″ = 0.67216061563 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     