# 15 17 20 triangle

### Acute scalene triangle.

Sides: a = 15   b = 17   c = 20

Area: T = 124.2743891063
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 46.97222150901° = 46°58'20″ = 0.82198198103 rad
Angle ∠ B = β = 55.94442022574° = 55°56'39″ = 0.97664105268 rad
Angle ∠ C = γ = 77.08435826525° = 77°5'1″ = 1.34553623165 rad

Height: ha = 16.57698521418
Height: hb = 14.62204577721
Height: hc = 12.42773891063

Median: ma = 16.97879268463
Median: mb = 15.5
Median: mc = 12.53299640861

Inradius: r = 4.78797650409
Circumradius: R = 10.26595966787

Vertex coordinates: A[20; 0] B[0; 0] C[8.4; 12.42773891063]
Centroid: CG[9.46766666667; 4.14224630354]
Coordinates of the circumscribed circle: U[10; 2.29333216105]
Coordinates of the inscribed circle: I[9; 4.78797650409]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 133.028778491° = 133°1'40″ = 0.82198198103 rad
∠ B' = β' = 124.0565797743° = 124°3'21″ = 0.97664105268 rad
∠ C' = γ' = 102.9166417347° = 102°54'59″ = 1.34553623165 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    