# 6 13 15 triangle

### Obtuse scalene triangle.

Sides: a = 6   b = 13   c = 15

Area: T = 38.67881592116
Perimeter: p = 34
Semiperimeter: s = 17

Angle ∠ A = α = 23.37219828432° = 23°22'19″ = 0.40879180533 rad
Angle ∠ B = β = 59.26221313279° = 59°15'44″ = 1.03443193134 rad
Angle ∠ C = γ = 97.3665885829° = 97°21'57″ = 1.69993552868 rad

Height: ha = 12.89327197372
Height: hb = 5.95504860326
Height: hc = 5.15770878949

Median: ma = 13.71113092008
Median: mb = 9.3944147114
Median: mc = 6.80107352544

Inradius: r = 2.2755185836
Circumradius: R = 7.56224074662

Vertex coordinates: A[15; 0] B[0; 0] C[3.06766666667; 5.15770878949]
Centroid: CG[6.02222222222; 1.71990292983]
Coordinates of the circumscribed circle: U[7.5; -0.97695394187]
Coordinates of the inscribed circle: I[4; 2.2755185836]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.6288017157° = 156°37'41″ = 0.40879180533 rad
∠ B' = β' = 120.7387868672° = 120°44'16″ = 1.03443193134 rad
∠ C' = γ' = 82.6344114171° = 82°38'3″ = 1.69993552868 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    