# 5 10 12 triangle

### Obtuse scalene triangle.

Sides: a = 5   b = 10   c = 12

Area: T = 24.54546022579
Perimeter: p = 27
Semiperimeter: s = 13.5

Angle ∠ A = α = 24.14768479965° = 24°8'49″ = 0.42114420015 rad
Angle ∠ B = β = 54.99003678046° = 54°54'1″ = 0.95881921787 rad
Angle ∠ C = γ = 100.9532784199° = 100°57'10″ = 1.76219584733 rad

Height: ha = 9.81878409032
Height: hb = 4.90989204516
Height: hc = 4.0910767043

Median: ma = 10.75987173957
Median: mb = 7.71436243103
Median: mc = 5.14878150705

Inradius: r = 1.81881186858
Circumradius: R = 6.11113233135

Vertex coordinates: A[12; 0] B[0; 0] C[2.875; 4.0910767043]
Centroid: CG[4.95883333333; 1.36435890143]
Coordinates of the circumscribed circle: U[6; -1.16111514296]
Coordinates of the inscribed circle: I[3.5; 1.81881186858]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.8533152003° = 155°51'11″ = 0.42114420015 rad
∠ B' = β' = 125.1099632195° = 125°5'59″ = 0.95881921787 rad
∠ C' = γ' = 79.04772158011° = 79°2'50″ = 1.76219584733 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    