# 13 20 29 triangle

### Obtuse scalene triangle.

Sides: a = 13   b = 20   c = 29

Area: T = 110.7977111876
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 22.46112807045° = 22°27'41″ = 0.39220233025 rad
Angle ∠ B = β = 365.999846642° = 35°59'59″ = 0.62883158541 rad
Angle ∠ C = γ = 121.5398872654° = 121°32'20″ = 2.1211253497 rad

Height: ha = 17.04657095193
Height: hb = 11.08797111876
Height: hc = 7.64111801294

Median: ma = 24.04768293128
Median: mb = 20.12546117975
Median: mc = 8.61768439698

Inradius: r = 3.57441003831
Circumradius: R = 17.01330788437

Vertex coordinates: A[29; 0] B[0; 0] C[10.51772413793; 7.64111801294]
Centroid: CG[13.17224137931; 2.54770600431]
Coordinates of the circumscribed circle: U[14.5; -8.89991489336]
Coordinates of the inscribed circle: I[11; 3.57441003831]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.5398719296° = 157°32'19″ = 0.39220233025 rad
∠ B' = β' = 1444.000153358° = 144°1″ = 0.62883158541 rad
∠ C' = γ' = 58.46111273465° = 58°27'40″ = 2.1211253497 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    