# 10 13 21 triangle

### Obtuse scalene triangle.

Sides: a = 10   b = 13   c = 21

Area: T = 48.74442304278
Perimeter: p = 44
Semiperimeter: s = 22

Angle ∠ A = α = 20.92222396826° = 20°55'20″ = 0.36551619694 rad
Angle ∠ B = β = 27.66604498993° = 27°39'38″ = 0.48327659233 rad
Angle ∠ C = γ = 131.4177310418° = 131°25'2″ = 2.29436647609 rad

Height: ha = 9.74988460856
Height: hb = 7.49991123735
Height: hc = 4.64223076598

Median: ma = 16.73332005307
Median: mb = 15.10879449297
Median: mc = 4.92444289009

Inradius: r = 2.21656468376
Circumradius: R = 14.00216570989

Vertex coordinates: A[21; 0] B[0; 0] C[8.85771428571; 4.64223076598]
Centroid: CG[9.95223809524; 1.54774358866]
Coordinates of the circumscribed circle: U[10.5; -9.26326346962]
Coordinates of the inscribed circle: I[9; 2.21656468376]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.0787760317° = 159°4'40″ = 0.36551619694 rad
∠ B' = β' = 152.3439550101° = 152°20'22″ = 0.48327659233 rad
∠ C' = γ' = 48.58326895819° = 48°34'58″ = 2.29436647609 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    