# 15 19 24 triangle

### Acute scalene triangle.

Sides: a = 15   b = 19   c = 24

Area: T = 142.4788068488
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 38.67551276498° = 38°40'30″ = 0.67550083161 rad
Angle ∠ B = β = 52.33301130357° = 52°19'48″ = 0.91333327704 rad
Angle ∠ C = γ = 88.99547593146° = 88°59'41″ = 1.55332515671 rad

Height: ha = 18.99770757984
Height: hb = 14.99876914198
Height: hc = 11.8733172374

Median: ma = 20.30439405042
Median: mb = 17.61439149538
Median: mc = 12.20765556157

Inradius: r = 4.91330368444
Circumradius: R = 12.00218471485

Vertex coordinates: A[24; 0] B[0; 0] C[9.16766666667; 11.8733172374]
Centroid: CG[11.05655555556; 3.95877241247]
Coordinates of the circumscribed circle: U[12; 0.21105587219]
Coordinates of the inscribed circle: I[10; 4.91330368444]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.325487235° = 141°19'30″ = 0.67550083161 rad
∠ B' = β' = 127.6769886964° = 127°40'12″ = 0.91333327704 rad
∠ C' = γ' = 91.00552406854° = 91°19″ = 1.55332515671 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    