# Triangle calculator VC

Please enter the coordinates of the three vertices

### Acute scalene triangle.

Sides: a = 12.04215945788   b = 10.63301458127   c = 8.6022325267

Area: T = 44.5
Perimeter: p = 31.27440656586
Semiperimeter: s = 15.63770328293

Angle ∠ A = α = 76.72436029577° = 76°43'25″ = 1.33990794856 rad
Angle ∠ B = β = 59.22659638988° = 59°13'33″ = 1.03436880727 rad
Angle ∠ C = γ = 44.05504331436° = 44°3'2″ = 0.76988250953 rad

Height: ha = 7.3911047707
Height: hb = 8.37224157286
Height: hc = 10.34660398482

Median: ma = 7.56663729752
Median: mb = 9.01438781887
Median: mc = 10.51218980208

Inradius: r = 2.84658084399
Circumradius: R = 6.18661305421

Vertex coordinates: A[2; -3] B[7; 4] C[-5; 5]
Centroid: CG[1.33333333333; 2]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[1.69546949136; 2.84658084399]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 103.2766397042° = 103°16'35″ = 1.33990794856 rad
∠ B' = β' = 120.7744036101° = 120°46'27″ = 1.03436880727 rad
∠ C' = γ' = 135.9549566856° = 135°56'58″ = 0.76988250953 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    