# 12 21 22 triangle

### Acute scalene triangle.

Sides: a = 12   b = 21   c = 22

Area: T = 123.4444066281
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 32.30325452092° = 32°18'9″ = 0.56437857707 rad
Angle ∠ B = β = 69.25876200455° = 69°15'27″ = 1.20987735019 rad
Angle ∠ C = γ = 78.44398347453° = 78°26'23″ = 1.3699033381 rad

Height: ha = 20.57440110468
Height: hb = 11.75765777411
Height: hc = 11.22221878437

Median: ma = 20.65218764281
Median: mb = 14.27441024236
Median: mc = 13.09658008537

Inradius: r = 4.48988751375
Circumradius: R = 11.22877571677

Vertex coordinates: A[22; 0] B[0; 0] C[4.25; 11.22221878437]
Centroid: CG[8.75; 3.74107292812]
Coordinates of the circumscribed circle: U[11; 2.25500068927]
Coordinates of the inscribed circle: I[6.5; 4.48988751375]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.6977454791° = 147°41'51″ = 0.56437857707 rad
∠ B' = β' = 110.7422379954° = 110°44'33″ = 1.20987735019 rad
∠ C' = γ' = 101.5660165255° = 101°33'37″ = 1.3699033381 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.