5 23 27 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 23   c = 27

Area: T = 37.31220288915
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 6.90217733189° = 6°54'6″ = 0.12204586686 rad
Angle ∠ B = β = 33.55773097619° = 33°33'26″ = 0.58656855435 rad
Angle ∠ C = γ = 139.5410916919° = 139°32'27″ = 2.43554484415 rad

Height: ha = 14.92548115566
Height: hb = 3.24545242514
Height: hc = 2.7643853992

Median: ma = 24.95549594269
Median: mb = 15.64444878472
Median: mc = 9.7343961167

Inradius: r = 1.35768010506
Circumradius: R = 20.80442827759

Vertex coordinates: A[27; 0] B[0; 0] C[4.16766666667; 2.7643853992]
Centroid: CG[10.38988888889; 0.9211284664]
Coordinates of the circumscribed circle: U[13.5; -15.82993455903]
Coordinates of the inscribed circle: I[4.5; 1.35768010506]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 173.0988226681° = 173°5'54″ = 0.12204586686 rad
∠ B' = β' = 146.4432690238° = 146°26'34″ = 0.58656855435 rad
∠ C' = γ' = 40.45990830808° = 40°27'33″ = 2.43554484415 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 = 5 ; ; b = 23 ; ; c = 27 ; ;

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

p = a+b+c = 5+23+27 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-5)(27.5-23)(27.5-27) } ; ; T = sqrt{ 1392.19 } = 37.31 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 37.31 }{ 5 } = 14.92 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 37.31 }{ 23 } = 3.24 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 37.31 }{ 27 } = 2.76 ; ;

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{ 5**2-23**2-27**2 }{ 2 * 23 * 27 } ) = 6° 54'6" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-5**2-27**2 }{ 2 * 5 * 27 } ) = 33° 33'26" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-5**2-23**2 }{ 2 * 23 * 5 } ) = 139° 32'27" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 37.31 }{ 27.5 } = 1.36 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 6° 54'6" } = 20.8 ; ;




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