# 12 21 29 triangle

### Obtuse scalene triangle.

Sides: a = 12   b = 21   c = 29

Area: T = 108.536570841
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 20.88216697934° = 20°52'54″ = 0.36444538912 rad
Angle ∠ B = β = 38.59218511434° = 38°35'31″ = 0.67435548669 rad
Angle ∠ C = γ = 120.5266479063° = 120°31'35″ = 2.10435838955 rad

Height: ha = 18.0899284735
Height: hb = 10.33767341343
Height: hc = 7.48552212696

Median: ma = 24.59767477525
Median: mb = 19.5511214796
Median: mc = 9.06991785736

Inradius: r = 3.50111518842
Circumradius: R = 16.83331697169

Vertex coordinates: A[29; 0] B[0; 0] C[9.37993103448; 7.48552212696]
Centroid: CG[12.79331034483; 2.49550737565]
Coordinates of the circumscribed circle: U[14.5; -8.55501814435]
Coordinates of the inscribed circle: I[10; 3.50111518842]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.1188330207° = 159°7'6″ = 0.36444538912 rad
∠ B' = β' = 141.4088148857° = 141°24'29″ = 0.67435548669 rad
∠ C' = γ' = 59.47435209368° = 59°28'25″ = 2.10435838955 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    