12 25 28 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 25   c = 28

Area: T = 149.9533117674
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 25.36884394418° = 25°22'6″ = 0.44327627944 rad
Angle ∠ B = β = 63.19990168207° = 63°11'56″ = 1.10330309275 rad
Angle ∠ C = γ = 91.43325437376° = 91°25'57″ = 1.59657989317 rad

Height: ha = 24.99221862789
Height: hb = 11.99662494139
Height: hc = 10.71109369767

Median: ma = 25.85553669477
Median: mb = 17.54328047928
Median: mc = 13.73295302177

Inradius: r = 4.61439420823
Circumradius: R = 14.00443770519

Vertex coordinates: A[28; 0] B[0; 0] C[5.41107142857; 10.71109369767]
Centroid: CG[11.13769047619; 3.57703123256]
Coordinates of the circumscribed circle: U[14; -0.35501094263]
Coordinates of the inscribed circle: I[7.5; 4.61439420823]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.6321560558° = 154°37'54″ = 0.44327627944 rad
∠ B' = β' = 116.8010983179° = 116°48'4″ = 1.10330309275 rad
∠ C' = γ' = 88.56774562624° = 88°34'3″ = 1.59657989317 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 = 12 ; ; b = 25 ; ; c = 28 ; ;

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

p = a+b+c = 12+25+28 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-12)(32.5-25)(32.5-28) } ; ; T = sqrt{ 22485.94 } = 149.95 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 149.95 }{ 12 } = 24.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 149.95 }{ 25 } = 12 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 149.95 }{ 28 } = 10.71 ; ;

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{ 12**2-25**2-28**2 }{ 2 * 25 * 28 } ) = 25° 22'6" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-12**2-28**2 }{ 2 * 12 * 28 } ) = 63° 11'56" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-12**2-25**2 }{ 2 * 25 * 12 } ) = 91° 25'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 149.95 }{ 32.5 } = 4.61 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 25° 22'6" } = 14 ; ;




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