# Triangle calculator VC

Please enter the coordinates of the three vertices

### Acute scalene triangle.

Sides: a = 11.3143708499   b = 12.16655250606   c = 7.21111025509

Area: T = 40
Perimeter: p = 30.69903361105
Semiperimeter: s = 15.34551680553

Angle ∠ A = α = 65.7722254682° = 65°46'20″ = 1.14879424007 rad
Angle ∠ B = β = 78.6990067526° = 78°41'24″ = 1.37334007669 rad
Angle ∠ C = γ = 35.5387677792° = 35°32'16″ = 0.6220249486 rad

Height: ha = 7.07110678119
Height: hb = 6.57659594922
Height: hc = 11.09440039245

Median: ma = 8.24662112512
Median: mb = 7.28801098893
Median: mc = 11.18803398875

Inradius: r = 2.60766837363
Circumradius: R = 6.20332249677

Vertex coordinates: A[7; 4] B[3; -2] C[-5; 6]
Centroid: CG[1.66766666667; 2.66766666667]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[0.52113367473; 2.60766837363]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 114.2287745318° = 114°13'40″ = 1.14879424007 rad
∠ B' = β' = 101.3109932474° = 101°18'36″ = 1.37334007669 rad
∠ C' = γ' = 144.4622322208° = 144°27'44″ = 0.6220249486 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    