8 19 23 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 19   c = 23

Area: T = 71.41442842854
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 19.07770172092° = 19°4'37″ = 0.33329567618 rad
Angle ∠ B = β = 50.91877927026° = 50°55'4″ = 0.88986831305 rad
Angle ∠ C = γ = 110.0055190088° = 110°19″ = 1.92199527613 rad

Height: ha = 17.85435710714
Height: hb = 7.51772930827
Height: hc = 6.2109937764

Median: ma = 20.71223151772
Median: mb = 14.36114066163
Median: mc = 8.95882364336

Inradius: r = 2.85765713714
Circumradius: R = 12.23884479344

Vertex coordinates: A[23; 0] B[0; 0] C[5.04334782609; 6.2109937764]
Centroid: CG[9.3487826087; 2.07699792547]
Coordinates of the circumscribed circle: U[11.5; -4.18768374512]
Coordinates of the inscribed circle: I[6; 2.85765713714]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.9232982791° = 160°55'23″ = 0.33329567618 rad
∠ B' = β' = 129.0822207297° = 129°4'56″ = 0.88986831305 rad
∠ C' = γ' = 69.99548099118° = 69°59'41″ = 1.92199527613 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 = 8 ; ; b = 19 ; ; c = 23 ; ;

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

p = a+b+c = 8+19+23 = 50 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 50 }{ 2 } = 25 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25 * (25-8)(25-19)(25-23) } ; ; T = sqrt{ 5100 } = 71.41 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 71.41 }{ 8 } = 17.85 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 71.41 }{ 19 } = 7.52 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 71.41 }{ 23 } = 6.21 ; ;

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{ 8**2-19**2-23**2 }{ 2 * 19 * 23 } ) = 19° 4'37" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-8**2-23**2 }{ 2 * 8 * 23 } ) = 50° 55'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-8**2-19**2 }{ 2 * 19 * 8 } ) = 110° 19" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 71.41 }{ 25 } = 2.86 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 19° 4'37" } = 12.24 ; ;




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