17.464 14.213 30.871 triangle

Obtuse scalene triangle.

Sides: a = 17.46442491966   b = 14.21326704036   c = 30.87106980809

Area: T = 54.55000000015
Perimeter: p = 62.54876176811
Semiperimeter: s = 31.27438088406

Angle ∠ A = α = 14.38546380547° = 14°23'5″ = 0.25110592958 rad
Angle ∠ B = β = 11.66442488932° = 11°39'51″ = 0.2043579548 rad
Angle ∠ C = γ = 153.9511113052° = 153°57'4″ = 2.68769538099 rad

Height: ha = 6.24113218442
Height: hb = 7.66992132377
Height: hc = 3.53108563388

Median: ma = 22.38986131773
Median: mb = 24.05220269416
Median: mc = 3.9055124838

Inradius: r = 1.74326722878
Circumradius: R = 35.14992094068

Vertex coordinates: A[30.87106980809; 0] B[0; 0] C[17.10435976776; 3.53108563388]
Centroid: CG[15.99114319195; 1.17769521129]
Coordinates of the circumscribed circle: U[15.43553490405; -31.5798741614]
Coordinates of the inscribed circle: I[17.0611138437; 1.74326722878]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.6155361945° = 165°36'55″ = 0.25110592958 rad
∠ B' = β' = 168.3365751107° = 168°20'9″ = 0.2043579548 rad
∠ C' = γ' = 26.0498886948° = 26°2'56″ = 2.68769538099 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 = 17.46 ; ; b = 14.21 ; ; c = 30.87 ; ;

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

p = a+b+c = 17.46+14.21+30.87 = 62.55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62.55 }{ 2 } = 31.27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.27 * (31.27-17.46)(31.27-14.21)(31.27-30.87) } ; ; T = sqrt{ 2970.25 } = 54.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 54.5 }{ 17.46 } = 6.24 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 54.5 }{ 14.21 } = 7.67 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 54.5 }{ 30.87 } = 3.53 ; ;

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{ 17.46**2-14.21**2-30.87**2 }{ 2 * 14.21 * 30.87 } ) = 14° 23'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14.21**2-17.46**2-30.87**2 }{ 2 * 17.46 * 30.87 } ) = 11° 39'51" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30.87**2-17.46**2-14.21**2 }{ 2 * 14.21 * 17.46 } ) = 153° 57'4" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 54.5 }{ 31.27 } = 1.74 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17.46 }{ 2 * sin 14° 23'5" } = 35.15 ; ;




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