# 10 12 21 triangle

### Obtuse scalene triangle.

Sides: a = 10   b = 12   c = 21

Area: T = 34.2770067114
Perimeter: p = 43
Semiperimeter: s = 21.5

Angle ∠ A = α = 15.78223998562° = 15°46'57″ = 0.27554548414 rad
Angle ∠ B = β = 19.04992993211° = 19°2'57″ = 0.33224729934 rad
Angle ∠ C = γ = 145.1688300823° = 145°10'6″ = 2.53436648189 rad

Height: ha = 6.85440134228
Height: hb = 5.71216778523
Height: hc = 3.26438159156

Median: ma = 16.35554272338
Median: mb = 15.31333928311
Median: mc = 3.42878273002

Inradius: r = 1.594395661
Circumradius: R = 18.38333897349

Vertex coordinates: A[21; 0] B[0; 0] C[9.45223809524; 3.26438159156]
Centroid: CG[10.15107936508; 1.08879386385]
Coordinates of the circumscribed circle: U[10.5; -15.09896990741]
Coordinates of the inscribed circle: I[9.5; 1.594395661]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.2187600144° = 164°13'3″ = 0.27554548414 rad
∠ B' = β' = 160.9510700679° = 160°57'3″ = 0.33224729934 rad
∠ C' = γ' = 34.83216991773° = 34°49'54″ = 2.53436648189 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    