9 22 28 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 22   c = 28

Area: T = 82.48329527842
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 15.53435026063° = 15°32'1″ = 0.27111107648 rad
Angle ∠ B = β = 40.89113435638° = 40°53'29″ = 0.71436885808 rad
Angle ∠ C = γ = 123.575515383° = 123°34'31″ = 2.1576793308 rad

Height: ha = 18.33295450632
Height: hb = 7.49884502531
Height: hc = 5.89216394846

Median: ma = 24.77439782837
Median: mb = 17.64993625947
Median: mc = 9.30105376189

Inradius: r = 2.79660322978
Circumradius: R = 16.80334721505

Vertex coordinates: A[28; 0] B[0; 0] C[6.80435714286; 5.89216394846]
Centroid: CG[11.60111904762; 1.96438798282]
Coordinates of the circumscribed circle: U[14; -9.29328292954]
Coordinates of the inscribed circle: I[7.5; 2.79660322978]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.4666497394° = 164°27'59″ = 0.27111107648 rad
∠ B' = β' = 139.1098656436° = 139°6'31″ = 0.71436885808 rad
∠ C' = γ' = 56.425484617° = 56°25'29″ = 2.1576793308 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 = 9 ; ; b = 22 ; ; c = 28 ; ;

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

p = a+b+c = 9+22+28 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-9)(29.5-22)(29.5-28) } ; ; T = sqrt{ 6803.44 } = 82.48 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 82.48 }{ 9 } = 18.33 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 82.48 }{ 22 } = 7.5 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 82.48 }{ 28 } = 5.89 ; ;

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{ 9**2-22**2-28**2 }{ 2 * 22 * 28 } ) = 15° 32'1" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-9**2-28**2 }{ 2 * 9 * 28 } ) = 40° 53'29" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-9**2-22**2 }{ 2 * 22 * 9 } ) = 123° 34'31" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 82.48 }{ 29.5 } = 2.8 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 15° 32'1" } = 16.8 ; ;




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