# Triangle calculator VC

Please enter the coordinates of the three vertices

### Right isosceles triangle.

Sides: a = 10.77703296143   b = 15.23215462117   c = 10.77703296143

Area: T = 58
Perimeter: p = 36.77222054403
Semiperimeter: s = 18.38661027201

Angle ∠ A = α = 45° = 0.78553981634 rad
Angle ∠ B = β = 90° = 1.57107963268 rad
Angle ∠ C = γ = 45° = 0.78553981634 rad

Height: ha = 10.77703296143
Height: hb = 7.61657731059
Height: hc = 10.77703296143

Median: ma = 12.04215945788
Median: mb = 7.61657731059
Median: mc = 12.04215945788

Inradius: r = 3.15545565084
Circumradius: R = 7.61657731059

Vertex coordinates: A[9; -3] B[-1; 1] C[-5; -9]
Centroid: CG[1; -3.66766666667]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[-0; 3.15545565084]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135° = 0.78553981634 rad
∠ B' = β' = 90° = 1.57107963268 rad
∠ C' = γ' = 135° = 0.78553981634 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    