# Triangle calculator VC

Please enter the coordinates of the three vertices

### Right isosceles triangle.

Sides: a = 3.60655512755   b = 3.60655512755   c = 5.09990195136

Area: T = 6.5
Perimeter: p = 12.31101220645
Semiperimeter: s = 6.15550610323

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

Height: ha = 3.60655512755
Height: hb = 3.60655512755
Height: hc = 2.55495097568

Median: ma = 4.03111288741
Median: mb = 4.03111288741
Median: mc = 2.55495097568

Vertex coordinates: A[-3; 1] B[2; 0] C[-1; -2]
Centroid: CG[-0.66766666667; -0.33333333333]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[1.05660415187; 1.05660415187]

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    