# 7 23 24 triangle

### Acute scalene triangle.

Sides: a = 7   b = 23   c = 24

Area: T = 80.498844719
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 16.95774262942° = 16°57'27″ = 0.29659629215 rad
Angle ∠ B = β = 73.3988450401° = 73°23'54″ = 1.28110446254 rad
Angle ∠ C = γ = 89.64441233048° = 89°38'39″ = 1.56545851067 rad

Height: ha = 232.99955634
Height: hb = 76.999864973
Height: hc = 6.70882039325

Median: ma = 23.24332785983
Median: mb = 13.42657215821
Median: mc = 12.04215945788

Inradius: r = 2.981142397
Circumradius: R = 122.0002314792

Vertex coordinates: A[24; 0] B[0; 0] C[2; 6.70882039325]
Centroid: CG[8.66766666667; 2.23660679775]
Coordinates of the circumscribed circle: U[12; 0.07545355992]
Coordinates of the inscribed circle: I[4; 2.981142397]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.0432573706° = 163°2'33″ = 0.29659629215 rad
∠ B' = β' = 106.6021549599° = 106°36'6″ = 1.28110446254 rad
∠ C' = γ' = 90.35658766952° = 90°21'21″ = 1.56545851067 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    