# 10 15 21 triangle

### Obtuse scalene triangle.

Sides: a = 10   b = 15   c = 21

Area: T = 69.16664658632
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 26.05497983877° = 26°2'59″ = 0.45546547513 rad
Angle ∠ B = β = 41.20329536038° = 41°12'11″ = 0.71991272019 rad
Angle ∠ C = γ = 112.7477248008° = 112°44'50″ = 1.96878107003 rad

Height: ha = 13.83332931726
Height: hb = 9.22221954484
Height: hc = 6.58772824632

Median: ma = 17.55499287748
Median: mb = 14.63772811683
Median: mc = 7.22884161474

Inradius: r = 3.00772376462
Circumradius: R = 11.38655752231

Vertex coordinates: A[21; 0] B[0; 0] C[7.52438095238; 6.58772824632]
Centroid: CG[9.50879365079; 2.19657608211]
Coordinates of the circumscribed circle: U[10.5; -4.40224224196]
Coordinates of the inscribed circle: I[8; 3.00772376462]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.9550201612° = 153°57'1″ = 0.45546547513 rad
∠ B' = β' = 138.7977046396° = 138°47'49″ = 0.71991272019 rad
∠ C' = γ' = 67.25327519916° = 67°15'10″ = 1.96878107003 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    