# 9 13 21 triangle

### Obtuse scalene triangle.

Sides: a = 9   b = 13   c = 21

Area: T = 33.79662645865
Perimeter: p = 43
Semiperimeter: s = 21.5

Angle ∠ A = α = 14.33550459687° = 14°20'6″ = 0.25501937506 rad
Angle ∠ B = β = 20.95548664178° = 20°57'18″ = 0.36657314133 rad
Angle ∠ C = γ = 144.7110087613° = 144°42'36″ = 2.52656674897 rad

Height: ha = 7.51102810192
Height: hb = 5.1999425321
Height: hc = 3.21986918654

Median: ma = 16.87545370307
Median: mb = 14.79901994577
Median: mc = 3.84105728739

Inradius: r = 1.57219192831
Circumradius: R = 18.17550855462

Vertex coordinates: A[21; 0] B[0; 0] C[8.40547619048; 3.21986918654]
Centroid: CG[9.80215873016; 1.07328972885]
Coordinates of the circumscribed circle: U[10.5; -14.83552193988]
Coordinates of the inscribed circle: I[8.5; 1.57219192831]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.6654954031° = 165°39'54″ = 0.25501937506 rad
∠ B' = β' = 159.0455133582° = 159°2'42″ = 0.36657314133 rad
∠ C' = γ' = 35.29899123865° = 35°17'24″ = 2.52656674897 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    