# 12 19 21 triangle

### Acute scalene triangle.

Sides: a = 12   b = 19   c = 21

Area: T = 112.8721608476
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 34.45659504613° = 34°27'21″ = 0.60113697825 rad
Angle ∠ B = β = 63.61222000388° = 63°36'44″ = 1.11102423351 rad
Angle ∠ C = γ = 81.93218494999° = 81°55'55″ = 1.4329980536 rad

Height: ha = 18.8121934746
Height: hb = 11.88112219449
Height: hc = 10.75496769977

Median: ma = 19.10549731745
Median: mb = 14.22114626533
Median: mc = 11.92768604419

Inradius: r = 4.34112157106
Circumradius: R = 10.60549698074

Vertex coordinates: A[21; 0] B[0; 0] C[5.33333333333; 10.75496769977]
Centroid: CG[8.77877777778; 3.58332256659]
Coordinates of the circumscribed circle: U[10.5; 1.48884168151]
Coordinates of the inscribed circle: I[7; 4.34112157106]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.5444049539° = 145°32'39″ = 0.60113697825 rad
∠ B' = β' = 116.3887799961° = 116°23'16″ = 1.11102423351 rad
∠ C' = γ' = 98.06881505001° = 98°4'5″ = 1.4329980536 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.