# 12 20 21 triangle

### Acute scalene triangle.

Sides: a = 12   b = 20   c = 21

Area: T = 117.2054682074
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 33.92657123692° = 33°55'33″ = 0.59221153819 rad
Angle ∠ B = β = 68.46553711739° = 68°27'55″ = 1.19549461506 rad
Angle ∠ C = γ = 77.60989164569° = 77°36'32″ = 1.35545311211 rad

Height: ha = 19.5344113679
Height: hb = 11.72204682074
Height: hc = 11.16223506737

Median: ma = 19.60986715511
Median: mb = 13.87444369255
Median: mc = 12.7188097342

Inradius: r = 4.42328181915
Circumradius: R = 10.7550423769

Vertex coordinates: A[21; 0] B[0; 0] C[4.40547619048; 11.16223506737]
Centroid: CG[8.46882539683; 3.72107835579]
Coordinates of the circumscribed circle: U[10.5; 2.30768617671]
Coordinates of the inscribed circle: I[6.5; 4.42328181915]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.0744287631° = 146°4'27″ = 0.59221153819 rad
∠ B' = β' = 111.5354628826° = 111°32'5″ = 1.19549461506 rad
∠ C' = γ' = 102.3911083543° = 102°23'28″ = 1.35545311211 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.