# 13 19 21 triangle

### Acute scalene triangle.

Sides: a = 13   b = 19   c = 21

Area: T = 121.479916488
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 37.51113170202° = 37°30'41″ = 0.65546959888 rad
Angle ∠ B = β = 62.86878756647° = 62°52'4″ = 1.09772514241 rad
Angle ∠ C = γ = 79.62108073151° = 79°37'15″ = 1.39896452407 rad

Height: ha = 18.68991022893
Height: hb = 12.78772805137
Height: hc = 11.56994442743

Median: ma = 18.94106969249
Median: mb = 14.65443508898
Median: mc = 12.44398553046

Inradius: r = 4.58441194294
Circumradius: R = 10.67546700249

Vertex coordinates: A[21; 0] B[0; 0] C[5.92985714286; 11.56994442743]
Centroid: CG[8.97661904762; 3.85664814248]
Coordinates of the circumscribed circle: U[10.5; 1.9233169296]
Coordinates of the inscribed circle: I[7.5; 4.58441194294]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.489868298° = 142°29'19″ = 0.65546959888 rad
∠ B' = β' = 117.1322124335° = 117°7'56″ = 1.09772514241 rad
∠ C' = γ' = 100.3799192685° = 100°22'45″ = 1.39896452407 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    