# Triangle calculator VC

Please enter the coordinates of the three vertices

### Right scalene triangle.

Sides: a = 24.18767732449   b = 25.4955097568   c = 8.06222577483

Area: T = 97.5
Perimeter: p = 57.74441285612
Semiperimeter: s = 28.87220642806

Angle ∠ A = α = 71.56550511771° = 71°33'54″ = 1.24990457724 rad
Angle ∠ B = β = 90° = 1.57107963268 rad
Angle ∠ C = γ = 18.43549488229° = 18°26'6″ = 0.32217505544 rad

Height: ha = 8.06222577483
Height: hb = 7.64985292704
Height: hc = 24.18767732449

Median: ma = 14.53444418537
Median: mb = 12.7487548784
Median: mc = 24.52203996705

Inradius: r = 3.37769667126
Circumradius: R = 12.7487548784

Vertex coordinates: A[-7; 8] B[-11; 1] C[10; -11]
Centroid: CG[-2.66766666667; -0.66766666667]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[-0; 3.37769667126]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 108.4354948823° = 108°26'6″ = 1.24990457724 rad
∠ B' = β' = 90° = 1.57107963268 rad
∠ C' = γ' = 161.5655051177° = 161°33'54″ = 0.32217505544 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    