# 3 10 12 triangle

### Obtuse scalene triangle.

Sides: a = 3   b = 10   c = 12

Area: T = 12.1833492931
Perimeter: p = 25
Semiperimeter: s = 12.5

Angle ∠ A = α = 11.71658523949° = 11°42'57″ = 0.2044480199 rad
Angle ∠ B = β = 42.59988128925° = 42°35'56″ = 0.74334895424 rad
Angle ∠ C = γ = 125.6855334713° = 125°41'7″ = 2.19436229122 rad

Height: ha = 8.12223286207
Height: hb = 2.43766985862
Height: hc = 2.03105821552

Median: ma = 10.94330343141
Median: mb = 7.17663500472
Median: mc = 4.30111626335

Inradius: r = 0.97546794345
Circumradius: R = 7.3877044135

Vertex coordinates: A[12; 0] B[0; 0] C[2.20883333333; 2.03105821552]
Centroid: CG[4.73661111111; 0.67768607184]
Coordinates of the circumscribed circle: U[6; -4.30991090788]
Coordinates of the inscribed circle: I[2.5; 0.97546794345]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.2844147605° = 168°17'3″ = 0.2044480199 rad
∠ B' = β' = 137.4011187108° = 137°24'4″ = 0.74334895424 rad
∠ C' = γ' = 54.31546652873° = 54°18'53″ = 2.19436229122 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    