17 18 22 triangle

Acute scalene triangle.

Sides: a = 17   b = 18   c = 22

Area: T = 149.5622486941
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 49.05773686884° = 49°3'27″ = 0.8566212606 rad
Angle ∠ B = β = 53.11109502942° = 53°6'39″ = 0.92769609515 rad
Angle ∠ C = γ = 77.83216810174° = 77°49'54″ = 1.35884190961 rad

Height: ha = 17.5965586699
Height: hb = 16.61880541046
Height: hc = 13.59765897219

Median: ma = 18.21440056001
Median: mb = 17.47985582929
Median: mc = 13.62198384719

Inradius: r = 5.24878065593
Circumradius: R = 11.25328217097

Vertex coordinates: A[22; 0] B[0; 0] C[10.20545454545; 13.59765897219]
Centroid: CG[10.73548484848; 4.5322196574]
Coordinates of the circumscribed circle: U[11; 2.37219183015]
Coordinates of the inscribed circle: I[10.5; 5.24878065593]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.9432631312° = 130°56'33″ = 0.8566212606 rad
∠ B' = β' = 126.8899049706° = 126°53'21″ = 0.92769609515 rad
∠ C' = γ' = 102.1688318983° = 102°10'6″ = 1.35884190961 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 = 17 ; ; b = 18 ; ; c = 22 ; ;

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

p = a+b+c = 17+18+22 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-17)(28.5-18)(28.5-22) } ; ; T = sqrt{ 22368.94 } = 149.56 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 149.56 }{ 17 } = 17.6 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 149.56 }{ 18 } = 16.62 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 149.56 }{ 22 } = 13.6 ; ;

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{ 17**2-18**2-22**2 }{ 2 * 18 * 22 } ) = 49° 3'27" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-17**2-22**2 }{ 2 * 17 * 22 } ) = 53° 6'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-17**2-18**2 }{ 2 * 18 * 17 } ) = 77° 49'54" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 149.56 }{ 28.5 } = 5.25 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 49° 3'27" } = 11.25 ; ;




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