17 21 28 triangle

Obtuse scalene triangle.

Sides: a = 17   b = 21   c = 28

Area: T = 177.989876369
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 37.25879160013° = 37°15'29″ = 0.65502733067 rad
Angle ∠ B = β = 48.40546480534° = 48°24'17″ = 0.84548204818 rad
Angle ∠ C = γ = 94.33774359453° = 94°20'15″ = 1.64664988651 rad

Height: ha = 20.94398545518
Height: hb = 16.95113108276
Height: hc = 12.71334831207

Median: ma = 23.24332785983
Median: mb = 20.64658228221
Median: mc = 13

Inradius: r = 5.39435988997
Circumradius: R = 14.04402121358

Vertex coordinates: A[28; 0] B[0; 0] C[11.28657142857; 12.71334831207]
Centroid: CG[13.09552380952; 4.23878277069]
Coordinates of the circumscribed circle: U[14; -1.06218647834]
Coordinates of the inscribed circle: I[12; 5.39435988997]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.7422083999° = 142°44'31″ = 0.65502733067 rad
∠ B' = β' = 131.5955351947° = 131°35'43″ = 0.84548204818 rad
∠ C' = γ' = 85.66325640547° = 85°39'45″ = 1.64664988651 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 = 17 ; ; b = 21 ; ; c = 28 ; ;

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

p = a+b+c = 17+21+28 = 66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 66 }{ 2 } = 33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33 * (33-17)(33-21)(33-28) } ; ; T = sqrt{ 31680 } = 177.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 177.99 }{ 17 } = 20.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 177.99 }{ 21 } = 16.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 177.99 }{ 28 } = 12.71 ; ;

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{ 17**2-21**2-28**2 }{ 2 * 21 * 28 } ) = 37° 15'29" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-17**2-28**2 }{ 2 * 17 * 28 } ) = 48° 24'17" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-17**2-21**2 }{ 2 * 21 * 17 } ) = 94° 20'15" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 177.99 }{ 33 } = 5.39 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 37° 15'29" } = 14.04 ; ;




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