# 19 21 30 triangle

### Obtuse scalene triangle.

Sides: a = 19   b = 21   c = 30

Area: T = 197.9989898732
Perimeter: p = 70
Semiperimeter: s = 35

Angle ∠ A = α = 38.9422441269° = 38°56'33″ = 0.68796738189 rad
Angle ∠ B = β = 44.00334273489° = 44°12″ = 0.76880046894 rad
Angle ∠ C = γ = 97.05441313821° = 97°3'15″ = 1.69439141453 rad

Height: ha = 20.84110419718
Height: hb = 18.85661808316
Height: hc = 13.19993265821

Median: ma = 24.08883789409
Median: mb = 22.80989894559
Median: mc = 13.26664991614

Inradius: r = 5.65768542495
Circumradius: R = 15.11444074479

Vertex coordinates: A[30; 0] B[0; 0] C[13.66766666667; 13.19993265821]
Centroid: CG[14.55655555556; 4.43997755274]
Coordinates of the circumscribed circle: U[15; -1.85661553006]
Coordinates of the inscribed circle: I[14; 5.65768542495]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.0587558731° = 141°3'27″ = 0.68796738189 rad
∠ B' = β' = 135.9976572651° = 135°59'48″ = 0.76880046894 rad
∠ C' = γ' = 82.94658686179° = 82°56'45″ = 1.69439141453 rad

# How did we calculate this triangle?

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. ### 1. The triangle circumference is the sum of the lengths of its three sides ### 2. Semiperimeter of the triangle ### 3. The triangle area using Heron's formula ### 4. Calculate the heights of the triangle from its area. ### 5. Calculation of the inner angles of the triangle using a Law of Cosines    