# 21 22 30 triangle

### Acute scalene triangle.

Sides: a = 21   b = 22   c = 30

Area: T = 230.9155433655
Perimeter: p = 73
Semiperimeter: s = 36.5

Angle ∠ A = α = 44.40664477069° = 44°24'23″ = 0.77550387216 rad
Angle ∠ B = β = 47.14439519766° = 47°8'38″ = 0.82328171844 rad
Angle ∠ C = γ = 88.45496003164° = 88°26'59″ = 1.54437367476 rad

Height: ha = 21.99219460624
Height: hb = 20.99223121504
Height: hc = 15.39443622437

Median: ma = 24.11994941904
Median: mb = 23.44114163395
Median: mc = 15.41110350074

Inradius: r = 6.32664502371
Circumradius: R = 15.00554933322

Vertex coordinates: A[30; 0] B[0; 0] C[14.28333333333; 15.39443622437]
Centroid: CG[14.76111111111; 5.13114540812]
Coordinates of the circumscribed circle: U[15; 0.4065992785]
Coordinates of the inscribed circle: I[14.5; 6.32664502371]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.5943552293° = 135°35'37″ = 0.77550387216 rad
∠ B' = β' = 132.8566048023° = 132°51'22″ = 0.82328171844 rad
∠ C' = γ' = 91.55503996836° = 91°33'1″ = 1.54437367476 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    