# 12 13 21 triangle

### Obtuse scalene triangle.

Sides: a = 12   b = 13   c = 21

Area: T = 71.13436769751
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 31.40878008669° = 31°24'28″ = 0.54881695359 rad
Angle ∠ B = β = 34.37112560241° = 34°22'17″ = 0.65998915857 rad
Angle ∠ C = γ = 114.2210943109° = 114°13'15″ = 1.9943531532 rad

Height: ha = 11.85656128292
Height: hb = 10.94436426116
Height: hc = 6.77546359024

Median: ma = 16.40112194669
Median: mb = 15.81992920196
Median: mc = 6.80107352544

Inradius: r = 3.09327685641
Circumradius: R = 11.51435338819

Vertex coordinates: A[21; 0] B[0; 0] C[9.90547619048; 6.77546359024]
Centroid: CG[10.30215873016; 2.25882119675]
Coordinates of the circumscribed circle: U[10.5; -4.72435010798]
Coordinates of the inscribed circle: I[10; 3.09327685641]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.5922199133° = 148°35'32″ = 0.54881695359 rad
∠ B' = β' = 145.6298743976° = 145°37'43″ = 0.65998915857 rad
∠ C' = γ' = 65.7799056891° = 65°46'45″ = 1.9943531532 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 ### 6. Inradius ### 7. Circumradius ### 8. Calculation of medians #### Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.