8 24 27 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 24   c = 27

Area: T = 93.38659598655
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 16.75219148957° = 16°45'7″ = 0.29223760709 rad
Angle ∠ B = β = 59.847673455° = 59°50'48″ = 1.04545225645 rad
Angle ∠ C = γ = 103.4011350554° = 103°24'5″ = 1.80546940182 rad

Height: ha = 23.34664899664
Height: hb = 7.78221633221
Height: hc = 6.91774785086

Median: ma = 25.22989516231
Median: mb = 15.89902485821
Median: mc = 11.73766945943

Inradius: r = 3.16656257582
Circumradius: R = 13.87878891588

Vertex coordinates: A[27; 0] B[0; 0] C[4.01985185185; 6.91774785086]
Centroid: CG[10.34395061728; 2.30658261695]
Coordinates of the circumscribed circle: U[13.5; -3.21664899352]
Coordinates of the inscribed circle: I[5.5; 3.16656257582]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.2488085104° = 163°14'53″ = 0.29223760709 rad
∠ B' = β' = 120.153326545° = 120°9'12″ = 1.04545225645 rad
∠ C' = γ' = 76.59986494456° = 76°35'55″ = 1.80546940182 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 = 24 ; ; c = 27 ; ;

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

p = a+b+c = 8+24+27 = 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 * (29.5-8)(29.5-24)(29.5-27) } ; ; T = sqrt{ 8720.94 } = 93.39 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 93.39 }{ 8 } = 23.35 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 93.39 }{ 24 } = 7.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 93.39 }{ 27 } = 6.92 ; ;

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{ 8**2-24**2-27**2 }{ 2 * 24 * 27 } ) = 16° 45'7" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-8**2-27**2 }{ 2 * 8 * 27 } ) = 59° 50'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-8**2-24**2 }{ 2 * 24 * 8 } ) = 103° 24'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 93.39 }{ 29.5 } = 3.17 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 16° 45'7" } = 13.88 ; ;




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