# Triangle calculator VC

Please enter the coordinates of the three vertices

### Acute isosceles triangle.

Sides: a = 11.4021754251   b = 11.4021754251   c = 2.82884271247

Area: T = 16
Perimeter: p = 25.63219356267
Semiperimeter: s = 12.81659678134

Angle ∠ A = α = 82.87549836511° = 82°52'30″ = 1.44664413322 rad
Angle ∠ B = β = 82.87549836511° = 82°52'30″ = 1.44664413322 rad
Angle ∠ C = γ = 14.25500326978° = 14°15' = 0.24987099891 rad

Height: ha = 2.80765856618
Height: hb = 2.80765856618
Height: hc = 11.3143708499

Median: ma = 6.04215229868
Median: mb = 6.04215229868
Median: mc = 11.3143708499

Inradius: r = 1.24884425861
Circumradius: R = 5.74552425971

Vertex coordinates: A[2; 4] B[4; 2] C[-5; -5]
Centroid: CG[0.33333333333; 0.33333333333]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[0.15660553233; 1.24884425861]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 97.12550163489° = 97°7'30″ = 1.44664413322 rad
∠ B' = β' = 97.12550163489° = 97°7'30″ = 1.44664413322 rad
∠ C' = γ' = 165.7549967302° = 165°45' = 0.24987099891 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    