# 6 13 17 triangle

### Obtuse scalene triangle.

Sides: a = 6   b = 13   c = 17

Area: T = 32.86333534503
Perimeter: p = 36
Semiperimeter: s = 18

Angle ∠ A = α = 17.30218627088° = 17°18'7″ = 0.3021974471 rad
Angle ∠ B = β = 40.11991668984° = 40°7'9″ = 0.77002115555 rad
Angle ∠ C = γ = 122.5798970393° = 122°34'44″ = 2.13994066271 rad

Height: ha = 10.95444511501
Height: hb = 5.05659005308
Height: hc = 3.86662768765

Median: ma = 14.83223969742
Median: mb = 10.96658560997
Median: mc = 5.5

Inradius: r = 1.82657418584
Circumradius: R = 10.08772237674

Vertex coordinates: A[17; 0] B[0; 0] C[4.58882352941; 3.86662768765]
Centroid: CG[7.19660784314; 1.28987589588]
Coordinates of the circumscribed circle: U[8.5; -5.43215820286]
Coordinates of the inscribed circle: I[5; 1.82657418584]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.6988137291° = 162°41'53″ = 0.3021974471 rad
∠ B' = β' = 139.8810833102° = 139°52'51″ = 0.77002115555 rad
∠ C' = γ' = 57.42110296072° = 57°25'16″ = 2.13994066271 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    