13 18 28 triangle

Obtuse scalene triangle.

Sides: a = 13   b = 18   c = 28

Area: T = 91.63220768072
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 21.3232639967° = 21°19'22″ = 0.37221502726 rad
Angle ∠ B = β = 30.23300357169° = 30°13'48″ = 0.52876136563 rad
Angle ∠ C = γ = 128.4477324316° = 128°26'50″ = 2.24218287247 rad

Height: ha = 14.09772425857
Height: hb = 10.18113418675
Height: hc = 6.54551483434

Median: ma = 22.62218920517
Median: mb = 19.88771818014
Median: mc = 7.10663352018

Inradius: r = 3.10661720952
Circumradius: R = 17.87658362472

Vertex coordinates: A[28; 0] B[0; 0] C[11.23221428571; 6.54551483434]
Centroid: CG[13.07773809524; 2.18217161145]
Coordinates of the circumscribed circle: U[14; -11.11551033076]
Coordinates of the inscribed circle: I[11.5; 3.10661720952]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.6777360033° = 158°40'38″ = 0.37221502726 rad
∠ B' = β' = 149.7769964283° = 149°46'12″ = 0.52876136563 rad
∠ C' = γ' = 51.5532675684° = 51°33'10″ = 2.24218287247 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 = 13 ; ; b = 18 ; ; c = 28 ; ;

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

p = a+b+c = 13+18+28 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-13)(29.5-18)(29.5-28) } ; ; T = sqrt{ 8396.44 } = 91.63 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 91.63 }{ 13 } = 14.1 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 91.63 }{ 18 } = 10.18 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 91.63 }{ 28 } = 6.55 ; ;

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{ 13**2-18**2-28**2 }{ 2 * 18 * 28 } ) = 21° 19'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-13**2-28**2 }{ 2 * 13 * 28 } ) = 30° 13'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-13**2-18**2 }{ 2 * 18 * 13 } ) = 128° 26'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 91.63 }{ 29.5 } = 3.11 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 21° 19'22" } = 17.88 ; ;




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