# 15 18 19 triangle

### Acute scalene triangle.

Sides: a = 15   b = 18   c = 19

Area: T = 126.5544336156
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 47.73985577002° = 47°44'19″ = 0.8333195012 rad
Angle ∠ B = β = 62.63655316427° = 62°38'8″ = 1.09331962559 rad
Angle ∠ C = γ = 69.62659106571° = 69°37'33″ = 1.21552013857 rad

Height: ha = 16.87439114875
Height: hb = 14.06215929063
Height: hc = 13.32215090691

Median: ma = 16.91989243157
Median: mb = 14.56602197786
Median: mc = 13.57438719605

Inradius: r = 4.86774744676
Circumradius: R = 10.13439870205

Vertex coordinates: A[19; 0] B[0; 0] C[6.89547368421; 13.32215090691]
Centroid: CG[8.63215789474; 4.4410503023]
Coordinates of the circumscribed circle: U[9.5; 3.52881288146]
Coordinates of the inscribed circle: I[8; 4.86774744676]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.26114423° = 132°15'41″ = 0.8333195012 rad
∠ B' = β' = 117.3644468357° = 117°21'52″ = 1.09331962559 rad
∠ C' = γ' = 110.3744089343° = 110°22'27″ = 1.21552013857 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    