# Triangle calculator VC

Please enter the coordinates of the three vertices

### Acute scalene triangle.

Sides: a = 11.4021754251   b = 5.83109518948   c = 12.16655250606

Area: T = 33
Perimeter: p = 29.39882312064
Semiperimeter: s = 14.69991156032

Angle ∠ A = α = 68.4998565676° = 68°29'55″ = 1.19655255039 rad
Angle ∠ B = β = 28.41326614431° = 28°24'46″ = 0.49658944914 rad
Angle ∠ C = γ = 83.0898772881° = 83°5'20″ = 1.45501726582 rad

Height: ha = 5.78985829274
Height: hb = 11.31989066194
Height: hc = 5.42551665811

Median: ma = 7.64985292704
Median: mb = 11.42436596588
Median: mc = 6.70882039325

Vertex coordinates: A[-4; 2] B[8; 4] C[-1; -3]
Centroid: CG[1; 1]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[4.15499095351; 2.24550330272]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 111.5011434324° = 111°30'5″ = 1.19655255039 rad
∠ B' = β' = 151.5877338557° = 151°35'14″ = 0.49658944914 rad
∠ C' = γ' = 96.9111227119° = 96°54'40″ = 1.45501726582 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    