Triangle calculator VC

Please enter the coordinates of the three vertices

Acute isosceles triangle.

Sides: a = 2.44994897428   b = 3.74216573868   c = 3.74216573868

Area: T = 4.33301270189
Perimeter: p = 9.93328045163
Semiperimeter: s = 4.96664022582

Angle ∠ A = α = 38.21332107017° = 38°12'48″ = 0.66769463445 rad
Angle ∠ B = β = 70.89333946491° = 70°53'36″ = 1.23773231545 rad
Angle ∠ C = γ = 70.89333946491° = 70°53'36″ = 1.23773231545 rad

Height: ha = 3.53655339059
Height: hb = 2.31545502494
Height: hc = 2.31545502494

Median: ma = 3.53655339059
Median: mb = 2.55495097568
Median: mc = 2.55495097568

Inradius: r = 0.8721884071
Circumradius: R = 1.98798989873

Vertex coordinates: A[-2; 0; -1] B[-1; 2; 2] C[1; 1; 1]
Centroid: CG[-0.66766666667; 1; 0.66766666667]
Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.7876789298° = 141°47'12″ = 0.66769463445 rad
∠ B' = β' = 109.1076605351° = 109°6'24″ = 1.23773231545 rad
∠ C' = γ' = 109.1076605351° = 109°6'24″ = 1.23773231545 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     