# 12 20 23 triangle

### Acute scalene triangle.

Sides: a = 12   b = 20   c = 23

Area: T = 119.9411391938
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 31.43218690268° = 31°25'55″ = 0.54985896046 rad
Angle ∠ B = β = 60.35989156325° = 60°21'32″ = 1.05334618107 rad
Angle ∠ C = γ = 88.20992153407° = 88°12'33″ = 1.54395412383 rad

Height: ha = 19.99902319896
Height: hb = 11.99441391938
Height: hc = 10.43296862555

Median: ma = 20.77002415445
Median: mb = 15.37985564992
Median: mc = 11.82215904175

Inradius: r = 4.36215051614
Circumradius: R = 11.50656193504

Vertex coordinates: A[23; 0] B[0; 0] C[5.93547826087; 10.43296862555]
Centroid: CG[9.64549275362; 3.47765620852]
Coordinates of the circumscribed circle: U[11.5; 0.36595506047]
Coordinates of the inscribed circle: I[7.5; 4.36215051614]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.5688130973° = 148°34'5″ = 0.54985896046 rad
∠ B' = β' = 119.6411084367° = 119°38'28″ = 1.05334618107 rad
∠ C' = γ' = 91.79107846593° = 91°47'27″ = 1.54395412383 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.