# 6 17 20 triangle

### Obtuse scalene triangle.

Sides: a = 6   b = 17   c = 20

Area: T = 47.42882352613
Perimeter: p = 43
Semiperimeter: s = 21.5

Angle ∠ A = α = 16.2199911287° = 16°12' = 0.28327417905 rad
Angle ∠ B = β = 52.23295104114° = 52°13'46″ = 0.91215769234 rad
Angle ∠ C = γ = 111.5710578302° = 111°34'14″ = 1.94772739397 rad

Height: ha = 15.80994117538
Height: hb = 5.58797923837
Height: hc = 4.74328235261

Median: ma = 18.3176659084
Median: mb = 12.07326964676
Median: mc = 7.90656941504

Inradius: r = 2.20659644308
Circumradius: R = 10.75330882646

Vertex coordinates: A[20; 0] B[0; 0] C[3.675; 4.74328235261]
Centroid: CG[7.89216666667; 1.58109411754]
Coordinates of the circumscribed circle: U[10; -3.95333412738]
Coordinates of the inscribed circle: I[4.5; 2.20659644308]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.8800088713° = 163°48' = 0.28327417905 rad
∠ B' = β' = 127.7770489589° = 127°46'14″ = 0.91215769234 rad
∠ C' = γ' = 68.42994216984° = 68°25'46″ = 1.94772739397 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    