# Triangle calculator VC

Please enter the coordinates of the three vertices

### Acute scalene triangle.

Sides: a = 9.22195444573   b = 8.06222577483   c = 7.07110678119

Area: T = 27.5
Perimeter: p = 24.35328700175
Semiperimeter: s = 12.17664350087

Angle ∠ A = α = 74.74548812969° = 74°44'42″ = 1.30545442776 rad
Angle ∠ B = β = 57.52988077092° = 57°31'44″ = 1.00440671093 rad
Angle ∠ C = γ = 47.72663109939° = 47°43'35″ = 0.83329812667 rad

Height: ha = 5.966558759
Height: hb = 6.82219104024
Height: hc = 7.77881745931

Median: ma = 6.02107972894
Median: mb = 7.15989105316
Median: mc = 7.90656941504

Inradius: r = 2.25884607055
Circumradius: R = 4.7788135464

Vertex coordinates: A[-4; 5] B[1; 10] C[3; 1]
Centroid: CG[0; 5.33333333333]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[1.43772022671; 2.25884607055]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 105.2555118703° = 105°15'18″ = 1.30545442776 rad
∠ B' = β' = 122.4711192291° = 122°28'16″ = 1.00440671093 rad
∠ C' = γ' = 132.2743689006° = 132°16'25″ = 0.83329812667 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    