12 17 28 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 17   c = 28

Area: T = 51.9999399035
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 12.62200576915° = 12°37'12″ = 0.22202615585 rad
Angle ∠ B = β = 18.03303198517° = 18°1'49″ = 0.31546884466 rad
Angle ∠ C = γ = 149.3549622457° = 149°20'59″ = 2.60766426485 rad

Height: ha = 8.66765665058
Height: hb = 6.11875763571
Height: hc = 3.71442427882

Median: ma = 22.37218573212
Median: mb = 19.79326754129
Median: mc = 4.52876925691

Inradius: r = 1.8254540317
Circumradius: R = 27.46218558387

Vertex coordinates: A[28; 0] B[0; 0] C[11.41107142857; 3.71442427882]
Centroid: CG[13.13769047619; 1.23880809294]
Coordinates of the circumscribed circle: U[14; -23.62552730377]
Coordinates of the inscribed circle: I[11.5; 1.8254540317]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.3879942308° = 167°22'48″ = 0.22202615585 rad
∠ B' = β' = 161.9769680148° = 161°58'11″ = 0.31546884466 rad
∠ C' = γ' = 30.65503775432° = 30°39'1″ = 2.60766426485 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 = 17 ; ; c = 28 ; ;

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

p = a+b+c = 12+17+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 * (28.5-12)(28.5-17)(28.5-28) } ; ; T = sqrt{ 2703.94 } = 52 ; ;

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 }{ 12 } = 8.67 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 52 }{ 17 } = 6.12 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 52 }{ 28 } = 3.71 ; ;

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**2-17**2-28**2 }{ 2 * 17 * 28 } ) = 12° 37'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-12**2-28**2 }{ 2 * 12 * 28 } ) = 18° 1'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-12**2-17**2 }{ 2 * 17 * 12 } ) = 149° 20'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 52 }{ 28.5 } = 1.82 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 12° 37'12" } = 27.46 ; ;




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