5 20 22 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 20   c = 22

Area: T = 47.77548626372
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 12.5422190673° = 12°32'32″ = 0.21989025227 rad
Angle ∠ B = β = 60.33002719553° = 60°18'1″ = 1.05224382855 rad
Angle ∠ C = γ = 107.1587537372° = 107°9'27″ = 1.87702518455 rad

Height: ha = 19.11099450549
Height: hb = 4.77774862637
Height: hc = 4.34331693307

Median: ma = 20.87546257451
Median: mb = 12.43298028947
Median: mc = 9.56655632349

Inradius: r = 2.03329728782
Circumradius: R = 11.51223303269

Vertex coordinates: A[22; 0] B[0; 0] C[2.47772727273; 4.34331693307]
Centroid: CG[8.15990909091; 1.44877231102]
Coordinates of the circumscribed circle: U[11; -3.39661374464]
Coordinates of the inscribed circle: I[3.5; 2.03329728782]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.4587809327° = 167°27'28″ = 0.21989025227 rad
∠ B' = β' = 119.7699728045° = 119°41'59″ = 1.05224382855 rad
∠ C' = γ' = 72.84224626283° = 72°50'33″ = 1.87702518455 rad

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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.

a = 5 ; ; b = 20 ; ; c = 22 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 5+20+22 = 47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 47 }{ 2 } = 23.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23.5 * (23.5-5)(23.5-20)(23.5-22) } ; ; T = sqrt{ 2282.44 } = 47.77 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 47.77 }{ 5 } = 19.11 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 47.77 }{ 20 } = 4.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 47.77 }{ 22 } = 4.34 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 5**2-20**2-22**2 }{ 2 * 20 * 22 } ) = 12° 32'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-5**2-22**2 }{ 2 * 5 * 22 } ) = 60° 18'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-5**2-20**2 }{ 2 * 20 * 5 } ) = 107° 9'27" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 47.77 }{ 23.5 } = 2.03 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 12° 32'32" } = 11.51 ; ;




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