# 9 15 23 triangle

### Obtuse scalene triangle.

Sides: a = 9   b = 15   c = 23

Area: T = 38.05550587964
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 12.74548071461° = 12°44'41″ = 0.22224388472 rad
Angle ∠ B = β = 21.57327142774° = 21°34'22″ = 0.37765148927 rad
Angle ∠ C = γ = 145.6822478577° = 145°40'57″ = 2.54326389136 rad

Height: ha = 8.45766797325
Height: hb = 5.07440078395
Height: hc = 3.30991355475

Median: ma = 18.88878267675
Median: mb = 15.77218102956
Median: mc = 4.55552167896

Inradius: r = 1.61993642041
Circumradius: R = 20.39880764858

Vertex coordinates: A[23; 0] B[0; 0] C[8.37695652174; 3.30991355475]
Centroid: CG[10.45765217391; 1.10330451825]
Coordinates of the circumscribed circle: U[11.5; -16.84773002086]
Coordinates of the inscribed circle: I[8.5; 1.61993642041]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.2555192854° = 167°15'19″ = 0.22224388472 rad
∠ B' = β' = 158.4277285723° = 158°25'38″ = 0.37765148927 rad
∠ C' = γ' = 34.31875214235° = 34°19'3″ = 2.54326389136 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    