# 21 27 30 triangle

### Acute scalene triangle.

Sides: a = 21   b = 27   c = 30

Area: T = 275.3477053734
Perimeter: p = 78
Semiperimeter: s = 39

Angle ∠ A = α = 42.83334280661° = 42°50' = 0.74875843497 rad
Angle ∠ B = β = 60.9410718932° = 60°56'27″ = 1.06436161939 rad
Angle ∠ C = γ = 76.2265853002° = 76°13'33″ = 1.333039211 rad

Height: ha = 26.2243528927
Height: hb = 20.39660780544
Height: hc = 18.35664702489

Median: ma = 26.53877090194
Median: mb = 22.0966379794
Median: mc = 18.9743665961

Inradius: r = 7.0660180865
Circumradius: R = 15.44441456421

Vertex coordinates: A[30; 0] B[0; 0] C[10.2; 18.35664702489]
Centroid: CG[13.4; 6.11988234163]
Coordinates of the circumscribed circle: U[15; 3.67771775338]
Coordinates of the inscribed circle: I[12; 7.0660180865]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.1676571934° = 137°10' = 0.74875843497 rad
∠ B' = β' = 119.0599281068° = 119°3'33″ = 1.06436161939 rad
∠ C' = γ' = 103.7744146998° = 103°46'27″ = 1.333039211 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.