# 10 21 22 triangle

### Acute scalene triangle.

Sides: a = 10   b = 21   c = 22

Area: T = 104.0298541757
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 26.76655005768° = 26°45'56″ = 0.4677146111 rad
Angle ∠ B = β = 71.03444250112° = 71°2'4″ = 1.24397845987 rad
Angle ∠ C = γ = 82.22000744121° = 82°12' = 1.43546619439 rad

Height: ha = 20.80657083513
Height: hb = 9.90774801673
Height: hc = 9.45771401597

Median: ma = 20.91765006634
Median: mb = 13.48114687627
Median: mc = 12.22770192606

Inradius: r = 3.92656053493
Circumradius: R = 11.10327222001

Vertex coordinates: A[22; 0] B[0; 0] C[3.25; 9.45771401597]
Centroid: CG[8.41766666667; 3.15223800532]
Coordinates of the circumscribed circle: U[11; 1.50767980129]
Coordinates of the inscribed circle: I[5.5; 3.92656053493]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.2344499423° = 153°14'4″ = 0.4677146111 rad
∠ B' = β' = 108.9665574989° = 108°57'56″ = 1.24397845987 rad
∠ C' = γ' = 97.87999255879° = 97°48' = 1.43546619439 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    