12 17 23 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 17   c = 23

Area: T = 99.13662698511
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 30.47702492171° = 30°28'13″ = 0.53218061727 rad
Angle ∠ B = β = 45.92107901521° = 45°55'15″ = 0.80114689833 rad
Angle ∠ C = γ = 103.6098960631° = 103°36'32″ = 1.80883174976 rad

Height: ha = 16.52327116419
Height: hb = 11.66330905707
Height: hc = 8.62105452044

Median: ma = 19.31332079158
Median: mb = 16.2565768207
Median: mc = 9.17987798753

Inradius: r = 3.81329334558
Circumradius: R = 11.83221982637

Vertex coordinates: A[23; 0] B[0; 0] C[8.3487826087; 8.62105452044]
Centroid: CG[10.44992753623; 2.87435150681]
Coordinates of the circumscribed circle: U[11.5; -2.78440466503]
Coordinates of the inscribed circle: I[9; 3.81329334558]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.5329750783° = 149°31'47″ = 0.53218061727 rad
∠ B' = β' = 134.0799209848° = 134°4'45″ = 0.80114689833 rad
∠ C' = γ' = 76.39110393692° = 76°23'28″ = 1.80883174976 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 = 12 ; ; b = 17 ; ; c = 23 ; ;

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

p = a+b+c = 12+17+23 = 52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 52 }{ 2 } = 26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26 * (26-12)(26-17)(26-23) } ; ; T = sqrt{ 9828 } = 99.14 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 99.14 }{ 12 } = 16.52 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 99.14 }{ 17 } = 11.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 99.14 }{ 23 } = 8.62 ; ;

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{ 12**2-17**2-23**2 }{ 2 * 17 * 23 } ) = 30° 28'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-12**2-23**2 }{ 2 * 12 * 23 } ) = 45° 55'15" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-12**2-17**2 }{ 2 * 17 * 12 } ) = 103° 36'32" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 99.14 }{ 26 } = 3.81 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 30° 28'13" } = 11.83 ; ;




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