# 24 27 28 triangle

### Acute scalene triangle.

Sides: a = 24   b = 27   c = 28

Area: T = 296.6666374063
Perimeter: p = 79
Semiperimeter: s = 39.5

Angle ∠ A = α = 51.70551131611° = 51°42'18″ = 0.90224244648 rad
Angle ∠ B = β = 61.99985409159° = 61°59'55″ = 1.08220786704 rad
Angle ∠ C = γ = 66.29663459229° = 66°17'47″ = 1.15770895184 rad

Height: ha = 24.72221978386
Height: hb = 21.97552869677
Height: hc = 21.19904552903

Median: ma = 24.74987373415
Median: mb = 22.31103115173
Median: mc = 21.36658606192

Inradius: r = 7.51105411155
Circumradius: R = 15.29899027209

Vertex coordinates: A[28; 0] B[0; 0] C[11.26878571429; 21.19904552903]
Centroid: CG[13.08992857143; 7.06334850968]
Coordinates of the circumscribed circle: U[14; 6.14766352759]
Coordinates of the inscribed circle: I[12.5; 7.51105411155]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.2954886839° = 128°17'42″ = 0.90224244648 rad
∠ B' = β' = 118.0011459084° = 118°5″ = 1.08220786704 rad
∠ C' = γ' = 113.7043654077° = 113°42'13″ = 1.15770895184 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    