# 4 21 22 triangle

### Obtuse scalene triangle.

Sides: a = 4   b = 21   c = 22

Area: T = 41.45440408163
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 10.33880005321° = 10°20'17″ = 0.18804321474 rad
Angle ∠ B = β = 70.414364113° = 70°24'49″ = 1.2298949876 rad
Angle ∠ C = γ = 99.24883583379° = 99°14'54″ = 1.73222106302 rad

Height: ha = 20.72770204082
Height: hb = 3.94880038873
Height: hc = 3.76985491651

Median: ma = 21.41326131054
Median: mb = 11.82215904175
Median: mc = 10.36882206767

Inradius: r = 1.76440017369
Circumradius: R = 11.14548725119

Vertex coordinates: A[22; 0] B[0; 0] C[1.34109090909; 3.76985491651]
Centroid: CG[7.78803030303; 1.2566183055]
Coordinates of the circumscribed circle: U[11; -1.79111402251]
Coordinates of the inscribed circle: I[2.5; 1.76440017369]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.6621999468° = 169°39'43″ = 0.18804321474 rad
∠ B' = β' = 109.586635887° = 109°35'11″ = 1.2298949876 rad
∠ C' = γ' = 80.75216416621° = 80°45'6″ = 1.73222106302 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    