# 7 22 23 triangle

### Acute scalene triangle.

Sides: a = 7   b = 22   c = 23

Area: T = 76.99435062197
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 17.71773880236° = 17°43'3″ = 0.30992267559 rad
Angle ∠ B = β = 73.02767339276° = 73°1'36″ = 1.2754556949 rad
Angle ∠ C = γ = 89.25658780488° = 89°15'21″ = 1.55878089487 rad

Height: ha = 21.99881446342
Height: hb = 6.99994096563
Height: hc = 6.69550874974

Median: ma = 22.23217340754
Median: mb = 12.96114813968
Median: mc = 11.58766302263

Inradius: r = 2.96112887008
Circumradius: R = 11.50109699321

Vertex coordinates: A[23; 0] B[0; 0] C[2.04334782609; 6.69550874974]
Centroid: CG[8.3487826087; 2.23216958325]
Coordinates of the circumscribed circle: U[11.5; 0.14993632459]
Coordinates of the inscribed circle: I[4; 2.96112887008]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.2832611976° = 162°16'57″ = 0.30992267559 rad
∠ B' = β' = 106.9733266072° = 106°58'24″ = 1.2754556949 rad
∠ C' = γ' = 90.74441219512° = 90°44'39″ = 1.55878089487 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    