# 10 14 21 triangle

### Obtuse scalene triangle.

Sides: a = 10   b = 14   c = 21

Area: T = 59.8832697835
Perimeter: p = 45
Semiperimeter: s = 22.5

Angle ∠ A = α = 24.03994336346° = 24°2'22″ = 0.42195672672 rad
Angle ∠ B = β = 34.77219440319° = 34°46'19″ = 0.60768849107 rad
Angle ∠ C = γ = 121.1898622333° = 121°11'19″ = 2.11551404757 rad

Height: ha = 11.9776539567
Height: hb = 8.55546711193
Height: hc = 5.70331140795

Median: ma = 17.1321841699
Median: mb = 14.88328760661
Median: mc = 6.14441028637

Inradius: r = 2.66114532371
Circumradius: R = 12.27439961053

Vertex coordinates: A[21; 0] B[0; 0] C[8.21442857143; 5.70331140795]
Centroid: CG[9.73880952381; 1.90110380265]
Coordinates of the circumscribed circle: U[10.5; -6.35661765545]
Coordinates of the inscribed circle: I[8.5; 2.66114532371]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.9610566365° = 155°57'38″ = 0.42195672672 rad
∠ B' = β' = 145.2288055968° = 145°13'41″ = 0.60768849107 rad
∠ C' = γ' = 58.81113776665° = 58°48'41″ = 2.11551404757 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    