# 19 23 25 triangle

### Acute scalene triangle.

Sides: a = 19   b = 23   c = 25

Area: T = 208.2144282651
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 46.40442980945° = 46°24'15″ = 0.81099077888 rad
Angle ∠ B = β = 61.2465826369° = 61°14'45″ = 1.06989413232 rad
Angle ∠ C = γ = 72.35498755365° = 72°21' = 1.26327435415 rad

Height: ha = 21.91772929107
Height: hb = 18.10655897958
Height: hc = 16.65771426121

Median: ma = 22.06224114729
Median: mb = 18.99334199132
Median: mc = 16.9932645468

Inradius: r = 6.21553517209
Circumradius: R = 13.11774959048

Vertex coordinates: A[25; 0] B[0; 0] C[9.14; 16.65771426121]
Centroid: CG[11.38; 5.55223808707]
Coordinates of the circumscribed circle: U[12.5; 3.97772727858]
Coordinates of the inscribed circle: I[10.5; 6.21553517209]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 133.5965701906° = 133°35'45″ = 0.81099077888 rad
∠ B' = β' = 118.7544173631° = 118°45'15″ = 1.06989413232 rad
∠ C' = γ' = 107.6550124463° = 107°39' = 1.26327435415 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    