# 23 25 27 triangle

### Acute scalene triangle.

Sides: a = 23   b = 25   c = 27

Area: T = 267.1466378415
Perimeter: p = 75
Semiperimeter: s = 37.5

Angle ∠ A = α = 52.33301130357° = 52°19'48″ = 0.91333327704 rad
Angle ∠ B = β = 59.35986925825° = 59°21'31″ = 1.03660046252 rad
Angle ∠ C = γ = 68.31111943819° = 68°18'40″ = 1.19222552579 rad

Height: ha = 23.23301198621
Height: hb = 21.37217102732
Height: hc = 19.78986206233

Median: ma = 23.3439880034
Median: mb = 21.74328149052
Median: mc = 19.86883164863

Inradius: r = 7.12439034244
Circumradius: R = 14.52985518113

Vertex coordinates: A[27; 0] B[0; 0] C[11.72222222222; 19.78986206233]
Centroid: CG[12.90774074074; 6.59662068744]
Coordinates of the circumscribed circle: U[13.5; 5.36992474085]
Coordinates of the inscribed circle: I[12.5; 7.12439034244]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 127.6769886964° = 127°40'12″ = 0.91333327704 rad
∠ B' = β' = 120.6411307418° = 120°38'29″ = 1.03660046252 rad
∠ C' = γ' = 111.6898805618° = 111°41'20″ = 1.19222552579 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    