# 7 20 23 triangle

### Obtuse scalene triangle.

Sides: a = 7   b = 20   c = 23

Area: T = 67.0822039325
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 16.95774262942° = 16°57'27″ = 0.29659629215 rad
Angle ∠ B = β = 56.44110241068° = 56°26'28″ = 0.98550817039 rad
Angle ∠ C = γ = 106.6021549599° = 106°36'6″ = 1.86105480282 rad

Height: ha = 19.166629695
Height: hb = 6.70882039325
Height: hc = 5.83332208109

Median: ma = 21.26661703181
Median: mb = 13.74877270849
Median: mc = 9.60546863561

Inradius: r = 2.6833281573
Circumradius: R = 122.0002314792

Vertex coordinates: A[23; 0] B[0; 0] C[3.87695652174; 5.83332208109]
Centroid: CG[8.95765217391; 1.9444406937]
Coordinates of the circumscribed circle: U[11.5; -3.42986375655]
Coordinates of the inscribed circle: I[5; 2.6833281573]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.0432573706° = 163°2'33″ = 0.29659629215 rad
∠ B' = β' = 123.5598975893° = 123°33'32″ = 0.98550817039 rad
∠ C' = γ' = 73.3988450401° = 73°23'54″ = 1.86105480282 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    