# 7 21 24 triangle

### Obtuse scalene triangle.

Sides: a = 7   b = 21   c = 24

Area: T = 70.28551335632
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 16.1955116739° = 16°11'42″ = 0.28326581098 rad
Angle ∠ B = β = 56.796617747° = 56°47'46″ = 0.99112802994 rad
Angle ∠ C = γ = 107.0098705791° = 107°31″ = 1.86876542444 rad

Height: ha = 20.08114667323
Height: hb = 6.69438222441
Height: hc = 5.85770944636

Median: ma = 22.27766694099
Median: mb = 14.22114626533
Median: mc = 10.05498756211

Inradius: r = 2.70332743678
Circumradius: R = 12.54988841706

Vertex coordinates: A[24; 0] B[0; 0] C[3.83333333333; 5.85770944636]
Centroid: CG[9.27877777778; 1.95223648212]
Coordinates of the circumscribed circle: U[12; -3.67107620363]
Coordinates of the inscribed circle: I[5; 2.70332743678]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.8054883261° = 163°48'18″ = 0.28326581098 rad
∠ B' = β' = 123.204382253° = 123°12'14″ = 0.99112802994 rad
∠ C' = γ' = 72.9911294209° = 72°59'29″ = 1.86876542444 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    