# 13 14 23 triangle

### Obtuse scalene triangle.

Sides: a = 13   b = 14   c = 23

Area: T = 81.24403840464
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 30.30547140565° = 30°18'17″ = 0.52989170392 rad
Angle ∠ B = β = 32.9166344351° = 32°54'59″ = 0.57444985866 rad
Angle ∠ C = γ = 116.7798941592° = 116°46'44″ = 2.03881770278 rad

Height: ha = 12.49985206225
Height: hb = 11.60657691495
Height: hc = 7.06443812214

Median: ma = 17.89655301682
Median: mb = 17.32105080757
Median: mc = 7.08987234394

Inradius: r = 3.25496153619
Circumradius: R = 12.8821524531

Vertex coordinates: A[23; 0] B[0; 0] C[10.91330434783; 7.06443812214]
Centroid: CG[11.30443478261; 2.35547937405]
Coordinates of the circumscribed circle: U[11.5; -5.80437637997]
Coordinates of the inscribed circle: I[11; 3.25496153619]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.6955285943° = 149°41'43″ = 0.52989170392 rad
∠ B' = β' = 147.0843655649° = 147°5'1″ = 0.57444985866 rad
∠ C' = γ' = 63.22110584075° = 63°13'16″ = 2.03881770278 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    