# 12 23 28 triangle

### Obtuse scalene triangle.

Sides: a = 12   b = 23   c = 28

Area: T = 135.1811128491
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 24.82330451588° = 24°49'23″ = 0.43332438684 rad
Angle ∠ B = β = 53.57664263577° = 53°34'35″ = 0.93550850414 rad
Angle ∠ C = γ = 101.6010528484° = 101°36'2″ = 1.77332637438 rad

Height: ha = 22.53301880818
Height: hb = 11.75548807383
Height: hc = 9.65657948922

Median: ma = 24.91098374142
Median: mb = 18.21440056001
Median: mc = 11.85332695911

Inradius: r = 4.29114643965
Circumradius: R = 14.29219357278

Vertex coordinates: A[28; 0] B[0; 0] C[7.125; 9.65657948922]
Centroid: CG[11.70883333333; 3.21985982974]
Coordinates of the circumscribed circle: U[14; -2.87439218583]
Coordinates of the inscribed circle: I[8.5; 4.29114643965]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.1776954841° = 155°10'37″ = 0.43332438684 rad
∠ B' = β' = 126.4243573642° = 126°25'25″ = 0.93550850414 rad
∠ C' = γ' = 78.39994715165° = 78°23'58″ = 1.77332637438 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    