# 23 24 28 triangle

### Acute scalene triangle.

Sides: a = 23   b = 24   c = 28

Area: T = 264.0765628372
Perimeter: p = 75
Semiperimeter: s = 37.5

Angle ∠ A = α = 51.8087642172° = 51°48'28″ = 0.90442139336 rad
Angle ∠ B = β = 55.09658714869° = 55°5'45″ = 0.96216043617 rad
Angle ∠ C = γ = 73.09664863411° = 73°5'47″ = 1.27657743583 rad

Height: ha = 22.96330981193
Height: hb = 22.00663023643
Height: hc = 18.86325448837

Median: ma = 23.40440594769
Median: mb = 22.63884628453
Median: mc = 18.88112075885

Inradius: r = 7.04220167566
Circumradius: R = 14.63221719419

Vertex coordinates: A[28; 0] B[0; 0] C[13.16107142857; 18.86325448837]
Centroid: CG[13.72202380952; 6.28875149612]
Coordinates of the circumscribed circle: U[14; 4.25444630375]
Coordinates of the inscribed circle: I[13.5; 7.04220167566]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.1922357828° = 128°11'32″ = 0.90442139336 rad
∠ B' = β' = 124.9044128513° = 124°54'15″ = 0.96216043617 rad
∠ C' = γ' = 106.9043513659° = 106°54'13″ = 1.27657743583 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    