14 22 27 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 22   c = 27

Area: T = 153.5122010931
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 31.12328957773° = 31°7'22″ = 0.54331970041 rad
Angle ∠ B = β = 54.31546652873° = 54°18'53″ = 0.94879697414 rad
Angle ∠ C = γ = 94.56224389353° = 94°33'45″ = 1.65504259081 rad

Height: ha = 21.93302872758
Height: hb = 13.95656373573
Height: hc = 11.37112600689

Median: ma = 23.61114379062
Median: mb = 18.48797186126
Median: mc = 12.56598566871

Inradius: r = 4.87333971724
Circumradius: R = 13.54329142475

Vertex coordinates: A[27; 0] B[0; 0] C[8.16766666667; 11.37112600689]
Centroid: CG[11.72222222222; 3.7990420023]
Coordinates of the circumscribed circle: U[13.5; -1.07772772697]
Coordinates of the inscribed circle: I[9.5; 4.87333971724]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.8777104223° = 148°52'38″ = 0.54331970041 rad
∠ B' = β' = 125.6855334713° = 125°41'7″ = 0.94879697414 rad
∠ C' = γ' = 85.43875610647° = 85°26'15″ = 1.65504259081 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 = 14 ; ; b = 22 ; ; c = 27 ; ;

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

p = a+b+c = 14+22+27 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-14)(31.5-22)(31.5-27) } ; ; T = sqrt{ 23565.94 } = 153.51 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 153.51 }{ 14 } = 21.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 153.51 }{ 22 } = 13.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 153.51 }{ 27 } = 11.37 ; ;

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{ 14**2-22**2-27**2 }{ 2 * 22 * 27 } ) = 31° 7'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-14**2-27**2 }{ 2 * 14 * 27 } ) = 54° 18'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-14**2-22**2 }{ 2 * 22 * 14 } ) = 94° 33'45" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 153.51 }{ 31.5 } = 4.87 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 31° 7'22" } = 13.54 ; ;




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