16 17 27 triangle

Obtuse scalene triangle.

Sides: a = 16   b = 17   c = 27

Area: T = 127.9844374046
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 33.89545474135° = 33°53'40″ = 0.59215714508 rad
Angle ∠ B = β = 36.33660575146° = 36°20'10″ = 0.63441838408 rad
Angle ∠ C = γ = 109.7699395072° = 109°46'10″ = 1.91658373619 rad

Height: ha = 15.99880467558
Height: hb = 15.05769851819
Height: hc = 9.48803240034

Median: ma = 21.09550231097
Median: mb = 20.5
Median: mc = 9.5

Inradius: r = 4.26661458015
Circumradius: R = 14.34655012667

Vertex coordinates: A[27; 0] B[0; 0] C[12.88988888889; 9.48803240034]
Centroid: CG[13.29662962963; 3.16601080011]
Coordinates of the circumscribed circle: U[13.5; -4.85221548402]
Coordinates of the inscribed circle: I[13; 4.26661458015]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.1055452586° = 146°6'20″ = 0.59215714508 rad
∠ B' = β' = 143.6643942485° = 143°39'50″ = 0.63441838408 rad
∠ C' = γ' = 70.23106049282° = 70°13'50″ = 1.91658373619 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 = 16 ; ; b = 17 ; ; c = 27 ; ;

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

p = a+b+c = 16+17+27 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-16)(30-17)(30-27) } ; ; T = sqrt{ 16380 } = 127.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 127.98 }{ 16 } = 16 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 127.98 }{ 17 } = 15.06 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 127.98 }{ 27 } = 9.48 ; ;

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{ 16**2-17**2-27**2 }{ 2 * 17 * 27 } ) = 33° 53'40" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-16**2-27**2 }{ 2 * 16 * 27 } ) = 36° 20'10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-16**2-17**2 }{ 2 * 17 * 16 } ) = 109° 46'10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 127.98 }{ 30 } = 4.27 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 33° 53'40" } = 14.35 ; ;




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