# 10 22 24 triangle

### Acute scalene triangle.

Sides: a = 10   b = 22   c = 24

Area: T = 109.9821816679
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 24.62199773287° = 24°37'12″ = 0.43296996662 rad
Angle ∠ B = β = 66.42218215218° = 66°25'19″ = 1.15992794807 rad
Angle ∠ C = γ = 88.95882011495° = 88°57'30″ = 1.55326135067 rad

Height: ha = 21.99663633358
Height: hb = 9.99883469708
Height: hc = 9.16551513899

Median: ma = 22.47222050542
Median: mb = 14.73109198627
Median: mc = 12.16655250606

Inradius: r = 3.92879220242
Circumradius: R = 12.0021983963

Vertex coordinates: A[24; 0] B[0; 0] C[4; 9.16551513899]
Centroid: CG[9.33333333333; 3.05550504633]
Coordinates of the circumscribed circle: U[12; 0.21882178902]
Coordinates of the inscribed circle: I[6; 3.92879220242]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.3880022671° = 155°22'48″ = 0.43296996662 rad
∠ B' = β' = 113.5788178478° = 113°34'41″ = 1.15992794807 rad
∠ C' = γ' = 91.04217988505° = 91°2'30″ = 1.55326135067 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    