3 20 22 triangle

Obtuse scalene triangle.

Sides: a = 3   b = 20   c = 22

Area: T = 23.4198742494
Perimeter: p = 45
Semiperimeter: s = 22.5

Angle ∠ A = α = 6.11106462489° = 6°6'38″ = 0.10766508965 rad
Angle ∠ B = β = 45.20771662976° = 45°12'26″ = 0.78990138974 rad
Angle ∠ C = γ = 128.6822187453° = 128°40'56″ = 2.24659278597 rad

Height: ha = 15.6122494996
Height: hb = 2.34218742494
Height: hc = 2.12989765904

Median: ma = 20.97702169755
Median: mb = 12.10437184369
Median: mc = 9.13878334412

Inradius: r = 1.04108329997
Circumradius: R = 14.09112775348

Vertex coordinates: A[22; 0] B[0; 0] C[2.11436363636; 2.12989765904]
Centroid: CG[8.03878787879; 0.71096588635]
Coordinates of the circumscribed circle: U[11; -8.80770484593]
Coordinates of the inscribed circle: I[2.5; 1.04108329997]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 173.8899353751° = 173°53'22″ = 0.10766508965 rad
∠ B' = β' = 134.7932833702° = 134°47'34″ = 0.78990138974 rad
∠ C' = γ' = 51.31878125465° = 51°19'4″ = 2.24659278597 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 = 3 ; ; b = 20 ; ; c = 22 ; ;

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

p = a+b+c = 3+20+22 = 45 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 45 }{ 2 } = 22.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22.5 * (22.5-3)(22.5-20)(22.5-22) } ; ; T = sqrt{ 548.44 } = 23.42 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 23.42 }{ 3 } = 15.61 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 23.42 }{ 20 } = 2.34 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 23.42 }{ 22 } = 2.13 ; ;

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{ 3**2-20**2-22**2 }{ 2 * 20 * 22 } ) = 6° 6'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-3**2-22**2 }{ 2 * 3 * 22 } ) = 45° 12'26" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-3**2-20**2 }{ 2 * 20 * 3 } ) = 128° 40'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 23.42 }{ 22.5 } = 1.04 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 6° 6'38" } = 14.09 ; ;




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