5 24 28 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 24   c = 28

Area: T = 38.81992928838
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 6.63444037907° = 6°38'4″ = 0.11657921901 rad
Angle ∠ B = β = 33.68105053841° = 33°40'50″ = 0.58878357127 rad
Angle ∠ C = γ = 139.6855090825° = 139°41'6″ = 2.43879647508 rad

Height: ha = 15.52877171535
Height: hb = 3.23549410737
Height: hc = 2.77328066346

Median: ma = 25.95766947048
Median: mb = 16.14400123916
Median: mc = 10.22325241501

Inradius: r = 1.36220804521
Circumradius: R = 21.63987249122

Vertex coordinates: A[28; 0] B[0; 0] C[4.16107142857; 2.77328066346]
Centroid: CG[10.72202380952; 0.92442688782]
Coordinates of the circumscribed circle: U[14; -16.54995277456]
Coordinates of the inscribed circle: I[4.5; 1.36220804521]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 173.3665596209° = 173°21'56″ = 0.11657921901 rad
∠ B' = β' = 146.3199494616° = 146°19'10″ = 0.58878357127 rad
∠ C' = γ' = 40.31549091747° = 40°18'54″ = 2.43879647508 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 = 5 ; ; b = 24 ; ; c = 28 ; ;

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

p = a+b+c = 5+24+28 = 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 * (28.5-5)(28.5-24)(28.5-28) } ; ; T = sqrt{ 1506.94 } = 38.82 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 38.82 }{ 5 } = 15.53 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 38.82 }{ 24 } = 3.23 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 38.82 }{ 28 } = 2.77 ; ;

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{ 5**2-24**2-28**2 }{ 2 * 24 * 28 } ) = 6° 38'4" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-5**2-28**2 }{ 2 * 5 * 28 } ) = 33° 40'50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-5**2-24**2 }{ 2 * 24 * 5 } ) = 139° 41'6" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 38.82 }{ 28.5 } = 1.36 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 6° 38'4" } = 21.64 ; ;




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