# 8 20 21 triangle

### Acute scalene triangle.

Sides: a = 8   b = 20   c = 21

Area: T = 79.79330918062
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 22.33216450092° = 22°19'54″ = 0.39897607328 rad
Angle ∠ B = β = 71.79900431357° = 71°47'24″ = 1.25329726229 rad
Angle ∠ C = γ = 85.87883118551° = 85°52'42″ = 1.49988592979 rad

Height: ha = 19.94882729516
Height: hb = 7.97993091806
Height: hc = 7.59993420768

Median: ma = 20.11221853611
Median: mb = 12.34990890352
Median: mc = 11.03440382454

Inradius: r = 3.25768608901
Circumradius: R = 10.52772271194

Vertex coordinates: A[21; 0] B[0; 0] C[2.5; 7.59993420768]
Centroid: CG[7.83333333333; 2.53331140256]
Coordinates of the circumscribed circle: U[10.5; 0.75766444492]
Coordinates of the inscribed circle: I[4.5; 3.25768608901]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.6688354991° = 157°40'6″ = 0.39897607328 rad
∠ B' = β' = 108.2109956864° = 108°12'36″ = 1.25329726229 rad
∠ C' = γ' = 94.12216881449° = 94°7'18″ = 1.49988592979 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.