# 4 13 15 triangle

### Obtuse scalene triangle.

Sides: a = 4   b = 13   c = 15

Area: T = 24
Perimeter: p = 32
Semiperimeter: s = 16

Angle ∠ A = α = 14.25500326978° = 14°15' = 0.24987099891 rad
Angle ∠ B = β = 53.13301023542° = 53°7'48″ = 0.9277295218 rad
Angle ∠ C = γ = 112.6219864948° = 112°37'11″ = 1.96655874465 rad

Height: ha = 12
Height: hb = 3.69223076923
Height: hc = 3.2

Median: ma = 13.89224439894
Median: mb = 8.84659030065
Median: mc = 6.02107972894

Inradius: r = 1.5
Circumradius: R = 8.125

Vertex coordinates: A[15; 0] B[0; 0] C[2.4; 3.2]
Centroid: CG[5.8; 1.06766666667]
Coordinates of the circumscribed circle: U[7.5; -3.125]
Coordinates of the inscribed circle: I[3; 1.5]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.7549967302° = 165°45' = 0.24987099891 rad
∠ B' = β' = 126.8769897646° = 126°52'12″ = 0.9277295218 rad
∠ C' = γ' = 67.3880135052° = 67°22'49″ = 1.96655874465 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    