# 23 24 30 triangle

### Acute scalene triangle.

Sides: a = 23   b = 24   c = 30

Area: T = 271.2199995391
Perimeter: p = 77
Semiperimeter: s = 38.5

Angle ∠ A = α = 48.88799513313° = 48°52'48″ = 0.85331160889 rad
Angle ∠ B = β = 51.8211319262° = 51°49'17″ = 0.90444526438 rad
Angle ∠ C = γ = 79.29987294067° = 79°17'55″ = 1.38440239208 rad

Height: ha = 23.58326082949
Height: hb = 22.65999996159
Height: hc = 18.08799996927

Median: ma = 24.61219889485
Median: mb = 23.8855141825
Median: mc = 18.09769610709

Inradius: r = 7.04441557244
Circumradius: R = 15.26554869851

Vertex coordinates: A[30; 0] B[0; 0] C[14.21766666667; 18.08799996927]
Centroid: CG[14.73988888889; 6.02766665642]
Coordinates of the circumscribed circle: U[15; 2.8354623942]
Coordinates of the inscribed circle: I[14.5; 7.04441557244]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131.1220048669° = 131°7'12″ = 0.85331160889 rad
∠ B' = β' = 128.1798680738° = 128°10'43″ = 0.90444526438 rad
∠ C' = γ' = 100.7011270593° = 100°42'5″ = 1.38440239208 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    