Triangle calculator VC

Please enter the coordinates of the three vertices

Acute isosceles triangle.

Sides: a = 4.24326406871   b = 4.12331056256   c = 4.12331056256

Area: T = 7.5
Perimeter: p = 12.48988519384
Semiperimeter: s = 6.24444259692

Angle ∠ A = α = 61.92875130641° = 61°55'39″ = 1.08108390005 rad
Angle ∠ B = β = 59.03662434679° = 59°2'10″ = 1.03303768265 rad
Angle ∠ C = γ = 59.03662434679° = 59°2'10″ = 1.03303768265 rad

Height: ha = 3.53655339059
Height: hb = 3.63880343755
Height: hc = 3.63880343755

Median: ma = 3.53655339059
Median: mb = 3.64400549446
Median: mc = 3.64400549446

Inradius: r = 1.20110711692
Circumradius: R = 2.4044163056

Vertex coordinates: A[-1; 1] B[0; 5] C[3; 2]
Centroid: CG[0.66766666667; 2.66766666667]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[0.72106427015; 1.20110711692]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 118.0722486936° = 118°4'21″ = 1.08108390005 rad
∠ B' = β' = 120.9643756532° = 120°57'50″ = 1.03303768265 rad
∠ C' = γ' = 120.9643756532° = 120°57'50″ = 1.03303768265 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     