8 24 28 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 24   c = 28

Area: T = 88.99443818451
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 15.35988855808° = 15°21'32″ = 0.26880631228 rad
Angle ∠ B = β = 52.61768015821° = 52°37' = 0.91883364295 rad
Angle ∠ C = γ = 112.0244312837° = 112°1'28″ = 1.95551931013 rad

Height: ha = 22.24985954613
Height: hb = 7.41661984871
Height: hc = 6.35767415604

Median: ma = 25.76881974535
Median: mb = 16.73332005307
Median: mc = 11.13655287257

Inradius: r = 2.96664793948
Circumradius: R = 15.10220769192

Vertex coordinates: A[28; 0] B[0; 0] C[4.85771428571; 6.35767415604]
Centroid: CG[10.95223809524; 2.11989138535]
Coordinates of the circumscribed circle: U[14; -5.66332788447]
Coordinates of the inscribed circle: I[6; 2.96664793948]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.6411114419° = 164°38'28″ = 0.26880631228 rad
∠ B' = β' = 127.3833198418° = 127°23' = 0.91883364295 rad
∠ C' = γ' = 67.9765687163° = 67°58'32″ = 1.95551931013 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 = 24 ; ; c = 28 ; ;

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

p = a+b+c = 8+24+28 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-8)(30-24)(30-28) } ; ; T = sqrt{ 7920 } = 88.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 88.99 }{ 8 } = 22.25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 88.99 }{ 24 } = 7.42 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 88.99 }{ 28 } = 6.36 ; ;

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**2-24**2-28**2 }{ 2 * 24 * 28 } ) = 15° 21'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-8**2-28**2 }{ 2 * 8 * 28 } ) = 52° 37' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-8**2-24**2 }{ 2 * 24 * 8 } ) = 112° 1'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 88.99 }{ 30 } = 2.97 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 15° 21'32" } = 15.1 ; ;




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