Triangle calculator VC

Please enter the coordinates of the three vertices

Acute scalene triangle.

Sides: a = 4.69904157598   b = 2.44994897428   c = 4.24326406871

Area: T = 5.17220402164
Perimeter: p = 11.38325461897
Semiperimeter: s = 5.69112730949

Angle ∠ A = α = 84.47881672365° = 84°28'41″ = 1.47444221643 rad
Angle ∠ B = β = 31.31994807061° = 31°19'10″ = 0.54766280583 rad
Angle ∠ C = γ = 64.20223520573° = 64°12'8″ = 1.12105424309 rad

Height: ha = 2.20553653583
Height: hb = 4.22329531531
Height: hc = 2.43881231397

Median: ma = 2.55495097568
Median: mb = 4.30111626335
Median: mc = 3.08222070015

Inradius: r = 0.90987668313
Circumradius: R = 2.35661413093

Vertex coordinates: A[1; 3; 2] B[2; -1; 1] C[-1; 2; 3]
Centroid: CG[0.66766666667; 1.33333333333; 2]
Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 95.52218327635° = 95°31'19″ = 1.47444221643 rad
∠ B' = β' = 148.6810519294° = 148°40'50″ = 0.54766280583 rad
∠ C' = γ' = 115.7987647943° = 115°47'52″ = 1.12105424309 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     