6 18 23 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 18   c = 23

Area: T = 33.62994142084
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 9.3549766841° = 9°20'59″ = 0.16331842157 rad
Angle ∠ B = β = 29.16987062436° = 29°10'7″ = 0.50990899625 rad
Angle ∠ C = γ = 141.4821526915° = 141°28'54″ = 2.46993184754 rad

Height: ha = 11.21098047361
Height: hb = 3.73766015787
Height: hc = 2.92442968877

Median: ma = 20.43328167417
Median: mb = 14.19550695666
Median: mc = 6.91101374805

Inradius: r = 1.43110389025
Circumradius: R = 18.46659773183

Vertex coordinates: A[23; 0] B[0; 0] C[5.23991304348; 2.92442968877]
Centroid: CG[9.41330434783; 0.97547656292]
Coordinates of the circumscribed circle: U[11.5; -14.44879174389]
Coordinates of the inscribed circle: I[5.5; 1.43110389025]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.6550233159° = 170°39'1″ = 0.16331842157 rad
∠ B' = β' = 150.8311293756° = 150°49'53″ = 0.50990899625 rad
∠ C' = γ' = 38.51884730846° = 38°31'6″ = 2.46993184754 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 = 6 ; ; b = 18 ; ; c = 23 ; ;

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

p = a+b+c = 6+18+23 = 47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 47 }{ 2 } = 23.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23.5 * (23.5-6)(23.5-18)(23.5-23) } ; ; T = sqrt{ 1130.94 } = 33.63 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 33.63 }{ 6 } = 11.21 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 33.63 }{ 18 } = 3.74 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 33.63 }{ 23 } = 2.92 ; ;

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{ 6**2-18**2-23**2 }{ 2 * 18 * 23 } ) = 9° 20'59" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-6**2-23**2 }{ 2 * 6 * 23 } ) = 29° 10'7" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-6**2-18**2 }{ 2 * 18 * 6 } ) = 141° 28'54" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 33.63 }{ 23.5 } = 1.43 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 9° 20'59" } = 18.47 ; ;




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