8 23 28 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 23   c = 28

Area: T = 78.63880156159
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 14.13655915806° = 14°8'8″ = 0.24767126148 rad
Angle ∠ B = β = 44.59877538761° = 44°35'52″ = 0.77883776441 rad
Angle ∠ C = γ = 121.2676654543° = 121°16' = 2.11765023947 rad

Height: ha = 19.6659503904
Height: hb = 6.83880883144
Height: hc = 5.61770011154

Median: ma = 25.30881014697
Median: mb = 17.08106908525
Median: mc = 10.02549688279

Inradius: r = 2.66656954446
Circumradius: R = 16.37988466674

Vertex coordinates: A[28; 0] B[0; 0] C[5.69664285714; 5.61770011154]
Centroid: CG[11.23221428571; 1.87223337051]
Coordinates of the circumscribed circle: U[14; -8.50109774823]
Coordinates of the inscribed circle: I[6.5; 2.66656954446]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.8644408419° = 165°51'52″ = 0.24767126148 rad
∠ B' = β' = 135.4022246124° = 135°24'8″ = 0.77883776441 rad
∠ C' = γ' = 58.73333454567° = 58°44' = 2.11765023947 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 = 8 ; ; b = 23 ; ; c = 28 ; ;

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

p = a+b+c = 8+23+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 * (29.5-8)(29.5-23)(29.5-28) } ; ; T = sqrt{ 6183.94 } = 78.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 78.64 }{ 8 } = 19.66 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 78.64 }{ 23 } = 6.84 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 78.64 }{ 28 } = 5.62 ; ;

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{ 8**2-23**2-28**2 }{ 2 * 23 * 28 } ) = 14° 8'8" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-8**2-28**2 }{ 2 * 8 * 28 } ) = 44° 35'52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-8**2-23**2 }{ 2 * 23 * 8 } ) = 121° 16' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 78.64 }{ 29.5 } = 2.67 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 14° 8'8" } = 16.38 ; ;




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