# 12 21 21 triangle

### Acute isosceles triangle.

Sides: a = 12   b = 21   c = 21

Area: T = 120.7487670785
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 33.2033099198° = 33°12'11″ = 0.58795034029 rad
Angle ∠ B = β = 73.3988450401° = 73°23'54″ = 1.28110446254 rad
Angle ∠ C = γ = 73.3988450401° = 73°23'54″ = 1.28110446254 rad

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

Median: ma = 20.12546117975
Median: mb = 13.5
Median: mc = 13.5

Inradius: r = 4.4722135955
Circumradius: R = 10.95767330897

Vertex coordinates: A[21; 0] B[0; 0] C[3.42985714286; 11.549977817]
Centroid: CG[8.14328571429; 3.833325939]
Coordinates of the circumscribed circle: U[10.5; 3.13304951685]
Coordinates of the inscribed circle: I[6; 4.4722135955]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.7976900802° = 146°47'49″ = 0.58795034029 rad
∠ B' = β' = 106.6021549599° = 106°36'6″ = 1.28110446254 rad
∠ C' = γ' = 106.6021549599° = 106°36'6″ = 1.28110446254 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.