# 20 24 30 triangle

### Acute scalene triangle.

Sides: a = 20   b = 24   c = 30

Area: T = 239.2476734565
Perimeter: p = 74
Semiperimeter: s = 37

Angle ∠ A = α = 41.65496722739° = 41°38'59″ = 0.72769239136 rad
Angle ∠ B = β = 52.89109950542° = 52°53'28″ = 0.92331220084 rad
Angle ∠ C = γ = 85.45993326719° = 85°27'34″ = 1.49215467317 rad

Height: ha = 23.92546734565
Height: hb = 19.93772278804
Height: hc = 15.95497823043

Median: ma = 25.25986618806
Median: mb = 22.49444437584
Median: mc = 16.21772747402

Inradius: r = 6.46661279612
Circumradius: R = 15.04772273176

Vertex coordinates: A[30; 0] B[0; 0] C[12.06766666667; 15.95497823043]
Centroid: CG[14.02222222222; 5.31765941014]
Coordinates of the circumscribed circle: U[15; 1.19112388293]
Coordinates of the inscribed circle: I[13; 6.46661279612]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.3550327726° = 138°21'1″ = 0.72769239136 rad
∠ B' = β' = 127.1099004946° = 127°6'32″ = 0.92331220084 rad
∠ C' = γ' = 94.54106673281° = 94°32'26″ = 1.49215467317 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    