# 21 23 28 triangle

### Acute scalene triangle.

Sides: a = 21   b = 23   c = 28

Area: T = 236.9811011898
Perimeter: p = 72
Semiperimeter: s = 36

Angle ∠ A = α = 47.38988944466° = 47°23'20″ = 0.8277092237 rad
Angle ∠ B = β = 53.71325429149° = 53°42'45″ = 0.93774607235 rad
Angle ∠ C = γ = 78.89985626385° = 78°53'55″ = 1.37770396931 rad

Height: ha = 22.57696201807
Height: hb = 20.60770445128
Height: hc = 16.92772151355

Median: ma = 23.3721991785
Median: mb = 21.91546070008
Median: mc = 17

Inradius: r = 6.5832805886
Circumradius: R = 14.26769658338

Vertex coordinates: A[28; 0] B[0; 0] C[12.42985714286; 16.92772151355]
Centroid: CG[13.47661904762; 5.64224050452]
Coordinates of the circumscribed circle: U[14; 2.74770555332]
Coordinates of the inscribed circle: I[13; 6.5832805886]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.6111105553° = 132°36'40″ = 0.8277092237 rad
∠ B' = β' = 126.2877457085° = 126°17'15″ = 0.93774607235 rad
∠ C' = γ' = 101.1011437362° = 101°6'5″ = 1.37770396931 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    