14 17 23 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 17   c = 23

Area: T = 118.4910505949
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 37.30772854951° = 37°18'26″ = 0.65111349669 rad
Angle ∠ B = β = 47.38988944466° = 47°23'20″ = 0.8277092237 rad
Angle ∠ C = γ = 95.30438200583° = 95°18'14″ = 1.66333654497 rad

Height: ha = 16.92772151355
Height: hb = 13.94400595234
Height: hc = 10.30435222564

Median: ma = 18.9743665961
Median: mb = 17.03767250374
Median: mc = 10.5

Inradius: r = 4.38985372574
Circumradius: R = 11.54994485321

Vertex coordinates: A[23; 0] B[0; 0] C[9.47882608696; 10.30435222564]
Centroid: CG[10.82660869565; 3.43545074188]
Coordinates of the circumscribed circle: U[11.5; -1.06875960828]
Coordinates of the inscribed circle: I[10; 4.38985372574]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.6932714505° = 142°41'34″ = 0.65111349669 rad
∠ B' = β' = 132.6111105553° = 132°36'40″ = 0.8277092237 rad
∠ C' = γ' = 84.69661799417° = 84°41'46″ = 1.66333654497 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 = 17 ; ; c = 23 ; ;

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

p = a+b+c = 14+17+23 = 54 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 54 }{ 2 } = 27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27 * (27-14)(27-17)(27-23) } ; ; T = sqrt{ 14040 } = 118.49 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 118.49 }{ 14 } = 16.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 118.49 }{ 17 } = 13.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 118.49 }{ 23 } = 10.3 ; ;

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**2-17**2-23**2 }{ 2 * 17 * 23 } ) = 37° 18'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-14**2-23**2 }{ 2 * 14 * 23 } ) = 47° 23'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-14**2-17**2 }{ 2 * 17 * 14 } ) = 95° 18'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 118.49 }{ 27 } = 4.39 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 37° 18'26" } = 11.55 ; ;




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