# 21 21 30 triangle

### Obtuse isosceles triangle.

Sides: a = 21   b = 21   c = 30

Area: T = 220.4544076851
Perimeter: p = 72
Semiperimeter: s = 36

Angle ∠ A = α = 44.41553085972° = 44°24'55″ = 0.77551933733 rad
Angle ∠ B = β = 44.41553085972° = 44°24'55″ = 0.77551933733 rad
Angle ∠ C = γ = 91.16993828056° = 91°10'10″ = 1.5911205907 rad

Height: ha = 20.99656263667
Height: hb = 20.99656263667
Height: hc = 14.69769384567

Median: ma = 23.67696007571
Median: mb = 23.67696007571
Median: mc = 14.69769384567

Inradius: r = 6.1243724357
Circumradius: R = 15.00331246745

Vertex coordinates: A[30; 0] B[0; 0] C[15; 14.69769384567]
Centroid: CG[15; 4.89989794856]
Coordinates of the circumscribed circle: U[15; -0.30661862178]
Coordinates of the inscribed circle: I[15; 6.1243724357]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.5854691403° = 135°35'5″ = 0.77551933733 rad
∠ B' = β' = 135.5854691403° = 135°35'5″ = 0.77551933733 rad
∠ C' = γ' = 88.83106171944° = 88°49'50″ = 1.5911205907 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    