# 8 21 25 triangle

### Obtuse scalene triangle.

Sides: a = 8   b = 21   c = 25

Area: T = 78.46601809837
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 17.3911302046° = 17°23'29″ = 0.30435354819 rad
Angle ∠ B = β = 51.68438655263° = 51°41'2″ = 0.90220536236 rad
Angle ∠ C = γ = 110.9254832428° = 110°55'29″ = 1.93660035481 rad

Height: ha = 19.61550452459
Height: hb = 7.47223981889
Height: hc = 6.27768144787

Median: ma = 22.73876340018
Median: mb = 15.3055227865
Median: mc = 9.81107084352

Inradius: r = 2.9065932629
Circumradius: R = 13.38325844758

Vertex coordinates: A[25; 0] B[0; 0] C[4.96; 6.27768144787]
Centroid: CG[9.98766666667; 2.09222714929]
Coordinates of the circumscribed circle: U[12.5; -4.77994944556]
Coordinates of the inscribed circle: I[6; 2.9065932629]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.6098697954° = 162°36'31″ = 0.30435354819 rad
∠ B' = β' = 128.3166134474° = 128°18'58″ = 0.90220536236 rad
∠ C' = γ' = 69.07551675724° = 69°4'31″ = 1.93660035481 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    