5 25 28 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 25   c = 28

Area: T = 52.76436238331
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 8.67105787468° = 8°40'14″ = 0.15113301472 rad
Angle ∠ B = β = 48.91876668595° = 48°55'4″ = 0.85437743491 rad
Angle ∠ C = γ = 122.4121754394° = 122°24'42″ = 2.13664881573 rad

Height: ha = 21.10554495332
Height: hb = 4.22110899066
Height: hc = 3.76988302738

Median: ma = 26.42444205234
Median: mb = 15.75659512566
Median: mc = 11.35878166916

Inradius: r = 1.81994353046
Circumradius: R = 16.58333947033

Vertex coordinates: A[28; 0] B[0; 0] C[3.28657142857; 3.76988302738]
Centroid: CG[10.42985714286; 1.25662767579]
Coordinates of the circumscribed circle: U[14; -8.8898699561]
Coordinates of the inscribed circle: I[4; 1.81994353046]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 171.3299421253° = 171°19'46″ = 0.15113301472 rad
∠ B' = β' = 131.082233314° = 131°4'56″ = 0.85437743491 rad
∠ C' = γ' = 57.58882456063° = 57°35'18″ = 2.13664881573 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 = 25 ; ; c = 28 ; ;

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

p = a+b+c = 5+25+28 = 58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 58 }{ 2 } = 29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29 * (29-5)(29-25)(29-28) } ; ; T = sqrt{ 2784 } = 52.76 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 52.76 }{ 5 } = 21.11 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 52.76 }{ 25 } = 4.22 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 52.76 }{ 28 } = 3.77 ; ;

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**2-25**2-28**2 }{ 2 * 25 * 28 } ) = 8° 40'14" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-5**2-28**2 }{ 2 * 5 * 28 } ) = 48° 55'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-5**2-25**2 }{ 2 * 25 * 5 } ) = 122° 24'42" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 52.76 }{ 29 } = 1.82 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 8° 40'14" } = 16.58 ; ;




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