# Triangle calculator VC

Please enter the coordinates of the three vertices

### Acute scalene triangle.

Sides: a = 14.31878210633   b = 18.02877563773   c = 13.03884048104

Area: T = 92.5
Perimeter: p = 45.3843982251
Semiperimeter: s = 22.69219911255

Angle ∠ A = α = 51.9111227119° = 51°54'40″ = 0.9066021832 rad
Angle ∠ B = β = 82.3043948278° = 82°18'14″ = 1.43664748848 rad
Angle ∠ C = γ = 45.7854824603° = 45°47'5″ = 0.79990959368 rad

Height: ha = 12.92109604717
Height: hb = 10.26219536302
Height: hc = 14.18988522937

Median: ma = 14.00989257261
Median: mb = 10.3087764064
Median: mc = 14.91664338902

Inradius: r = 4.07663280529
Circumradius: R = 9.09658093241

Vertex coordinates: A[-9; -5] B[-8; 8] C[6; 5]
Centroid: CG[-3.66766666667; 2.66766666667]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[0.55108551423; 4.07663280529]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.0898772881° = 128°5'20″ = 0.9066021832 rad
∠ B' = β' = 97.6966051722° = 97°41'46″ = 1.43664748848 rad
∠ C' = γ' = 134.2155175397° = 134°12'55″ = 0.79990959368 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    