# 13 21 30 triangle

### Obtuse scalene triangle.

Sides: a = 13   b = 21   c = 30

Area: T = 115.6554658358
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 21.54404283647° = 21°32'26″ = 0.37659513973 rad
Angle ∠ B = β = 36.37773613942° = 36°22'38″ = 0.63549047295 rad
Angle ∠ C = γ = 122.0822210241° = 122°4'56″ = 2.13107365268 rad

Height: ha = 17.79330243628
Height: hb = 11.01547293675
Height: hc = 7.71103105572

Median: ma = 25.0654915719
Median: mb = 20.5977329924
Median: mc = 8.944427191

Inradius: r = 3.61442080737
Circumradius: R = 17.70435670596

Vertex coordinates: A[30; 0] B[0; 0] C[10.46766666667; 7.71103105572]
Centroid: CG[13.48988888889; 2.57701035191]
Coordinates of the circumscribed circle: U[15; -9.40329934932]
Coordinates of the inscribed circle: I[11; 3.61442080737]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.4659571635° = 158°27'34″ = 0.37659513973 rad
∠ B' = β' = 143.6232638606° = 143°37'22″ = 0.63549047295 rad
∠ C' = γ' = 57.91877897589° = 57°55'4″ = 2.13107365268 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    