# 12 21 27 triangle

### Obtuse scalene triangle.

Sides: a = 12   b = 21   c = 27

Area: T = 120.7487670785
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 25.20987652968° = 25°12'32″ = 0.44399759548 rad
Angle ∠ B = β = 48.19896851042° = 48°11'23″ = 0.84110686706 rad
Angle ∠ C = γ = 106.6021549599° = 106°36'6″ = 1.86105480282 rad

Height: ha = 20.12546117975
Height: hb = 11.549977817
Height: hc = 8.944427191

Median: ma = 23.43107490277
Median: mb = 18.06223918682
Median: mc = 10.5

Inradius: r = 4.02549223595
Circumradius: R = 14.08772282582

Vertex coordinates: A[27; 0] B[0; 0] C[8; 8.944427191]
Centroid: CG[11.66766666667; 2.981142397]
Coordinates of the circumscribed circle: U[13.5; -4.02549223595]
Coordinates of the inscribed circle: I[9; 4.02549223595]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.7911234703° = 154°47'28″ = 0.44399759548 rad
∠ B' = β' = 131.8110314896° = 131°48'37″ = 0.84110686706 rad
∠ C' = γ' = 73.3988450401° = 73°23'54″ = 1.86105480282 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 ### 6. Inradius ### 7. Circumradius ### 8. Calculation of medians #### Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.