# 12 20 22 triangle

### Acute scalene triangle.

Sides: a = 12   b = 20   c = 22

Area: T = 119.0598808998
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 32.76437577589° = 32°45'50″ = 0.57218354482 rad
Angle ∠ B = β = 64.41769980226° = 64°25'1″ = 1.12442887097 rad
Angle ∠ C = γ = 82.81992442185° = 82°49'9″ = 1.44554684956 rad

Height: ha = 19.8433134833
Height: hb = 11.90658808998
Height: hc = 10.82435280907

Median: ma = 20.14994416796
Median: mb = 14.62987388383
Median: mc = 12.28882057274

Inradius: r = 4.41095855184
Circumradius: R = 11.08769578749

Vertex coordinates: A[22; 0] B[0; 0] C[5.18218181818; 10.82435280907]
Centroid: CG[9.06106060606; 3.60878426969]
Coordinates of the circumscribed circle: U[11; 1.38658697344]
Coordinates of the inscribed circle: I[7; 4.41095855184]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.2366242241° = 147°14'10″ = 0.57218354482 rad
∠ B' = β' = 115.5833001977° = 115°34'59″ = 1.12442887097 rad
∠ C' = γ' = 97.18107557815° = 97°10'51″ = 1.44554684956 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.