# 12 15 23 triangle

### Obtuse scalene triangle.

Sides: a = 12   b = 15   c = 23

Area: T = 80.6232577483
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 27.86441830985° = 27°51'51″ = 0.48663217384 rad
Angle ∠ B = β = 35.74880169402° = 35°44'53″ = 0.62439205967 rad
Angle ∠ C = γ = 116.3887799961° = 116°23'16″ = 2.03113503185 rad

Height: ha = 13.43770962472
Height: hb = 10.75496769977
Height: hc = 7.01106589116

Median: ma = 18.46661853126
Median: mb = 16.74106690428
Median: mc = 7.22884161474

Inradius: r = 3.22549030993
Circumradius: R = 12.838759503

Vertex coordinates: A[23; 0] B[0; 0] C[9.73991304348; 7.01106589116]
Centroid: CG[10.91330434783; 2.33768863039]
Coordinates of the circumscribed circle: U[11.5; -5.70655977911]
Coordinates of the inscribed circle: I[10; 3.22549030993]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.1365816901° = 152°8'9″ = 0.48663217384 rad
∠ B' = β' = 144.252198306° = 144°15'7″ = 0.62439205967 rad
∠ C' = γ' = 63.61222000388° = 63°36'44″ = 2.03113503185 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    