# Triangle calculator VC

Please enter the coordinates of the three vertices

### Right isosceles triangle.

Sides: a = 10.81766538264   b = 10.81766538264   c = 15.29770585408

Area: T = 58.5
Perimeter: p = 36.93303661936
Semiperimeter: s = 18.46551830968

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

Height: ha = 10.81766538264
Height: hb = 10.81766538264
Height: hc = 7.64985292704

Median: ma = 12.09333866224
Median: mb = 12.09333866224
Median: mc = 7.64985292704

Inradius: r = 3.1688124556
Circumradius: R = 7.64985292704

Vertex coordinates: A[10; 6] B[7; -9] C[1; 0]
Centroid: CG[6; -1]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[3.1688124556; 3.1688124556]

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