# 4 17 20 triangle

### Obtuse scalene triangle.

Sides: a = 4   b = 17   c = 20

Area: T = 24.33297657202
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 8.22882116737° = 8°13'42″ = 0.14436093853 rad
Angle ∠ B = β = 37.46326510725° = 37°27'46″ = 0.65438466077 rad
Angle ∠ C = γ = 134.3099137254° = 134°18'33″ = 2.34441366606 rad

Height: ha = 12.16548828601
Height: hb = 2.86223253788
Height: hc = 2.4332976572

Median: ma = 18.45326420872
Median: mb = 11.65111801977
Median: mc = 7.24656883731

Inradius: r = 1.187681784
Circumradius: R = 13.97546516226

Vertex coordinates: A[20; 0] B[0; 0] C[3.175; 2.4332976572]
Centroid: CG[7.725; 0.81109921907]
Coordinates of the circumscribed circle: U[10; -9.76217051776]
Coordinates of the inscribed circle: I[3.5; 1.187681784]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 171.7721788326° = 171°46'18″ = 0.14436093853 rad
∠ B' = β' = 142.5377348927° = 142°32'14″ = 0.65438466077 rad
∠ C' = γ' = 45.69108627462° = 45°41'27″ = 2.34441366606 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    