# 21 22 24 triangle

### Acute scalene triangle.

Sides: a = 21   b = 22   c = 24

Area: T = 213.8898843795
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 54.11440117604° = 54°6'50″ = 0.94444676767 rad
Angle ∠ B = β = 58.07876244183° = 58°4'39″ = 1.01436457678 rad
Angle ∠ C = γ = 67.80883638213° = 67°48'30″ = 1.18334792091 rad

Height: ha = 20.37703660757
Height: hb = 19.4444440345
Height: hc = 17.82440703163

Median: ma = 20.48878012485
Median: mb = 19.6855019685
Median: mc = 17.84765682976

Inradius: r = 6.38547416058
Circumradius: R = 12.96600027323

Vertex coordinates: A[24; 0] B[0; 0] C[11.10441666667; 17.82440703163]
Centroid: CG[11.70113888889; 5.94113567721]
Coordinates of the circumscribed circle: U[12; 4.89550659671]
Coordinates of the inscribed circle: I[11.5; 6.38547416058]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.886598824° = 125°53'10″ = 0.94444676767 rad
∠ B' = β' = 121.9222375582° = 121°55'21″ = 1.01436457678 rad
∠ C' = γ' = 112.1921636179° = 112°11'30″ = 1.18334792091 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.