# 13 23 30 triangle

### Obtuse scalene triangle.

Sides: a = 13   b = 23   c = 30

Area: T = 140.7122472795
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 24.07106146226° = 24°4'14″ = 0.42201114781 rad
Angle ∠ B = β = 46.18769385396° = 46°11'13″ = 0.80661141489 rad
Angle ∠ C = γ = 109.7422446838° = 109°44'33″ = 1.91553670265 rad

Height: ha = 21.64880727376
Height: hb = 12.23658671995
Height: hc = 9.38108315196

Median: ma = 25.92877843249
Median: mb = 20.05661711201
Median: mc = 11.13655287257

Inradius: r = 4.26440143271
Circumradius: R = 15.93767535476

Vertex coordinates: A[30; 0] B[0; 0] C[9; 9.38108315196]
Centroid: CG[13; 3.12769438399]
Coordinates of the circumscribed circle: U[15; -5.3833318088]
Coordinates of the inscribed circle: I[10; 4.26440143271]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.9299385377° = 155°55'46″ = 0.42201114781 rad
∠ B' = β' = 133.813306146° = 133°48'47″ = 0.80661141489 rad
∠ C' = γ' = 70.25875531622° = 70°15'27″ = 1.91553670265 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    