10 14 23 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 14   c = 23

Area: T = 38.81992928838
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 13.95222764517° = 13°57'8″ = 0.24435131622 rad
Angle ∠ B = β = 19.72882289323° = 19°43'42″ = 0.34443225505 rad
Angle ∠ C = γ = 146.3199494616° = 146°19'10″ = 2.55437569409 rad

Height: ha = 7.76438585768
Height: hb = 5.54656132691
Height: hc = 3.37655906855

Median: ma = 18.37111730709
Median: mb = 16.29441707368
Median: mc = 3.96986269666

Inradius: r = 1.65218848036
Circumradius: R = 20.73771113742

Vertex coordinates: A[23; 0] B[0; 0] C[9.41330434783; 3.37655906855]
Centroid: CG[10.80443478261; 1.12551968952]
Coordinates of the circumscribed circle: U[11.5; -17.25662391078]
Coordinates of the inscribed circle: I[9.5; 1.65218848036]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.0487723548° = 166°2'52″ = 0.24435131622 rad
∠ B' = β' = 160.2721771068° = 160°16'18″ = 0.34443225505 rad
∠ C' = γ' = 33.68105053841° = 33°40'50″ = 2.55437569409 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 = 10 ; ; b = 14 ; ; c = 23 ; ;

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

p = a+b+c = 10+14+23 = 47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 47 }{ 2 } = 23.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23.5 * (23.5-10)(23.5-14)(23.5-23) } ; ; T = sqrt{ 1506.94 } = 38.82 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 38.82 }{ 10 } = 7.76 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 38.82 }{ 14 } = 5.55 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 38.82 }{ 23 } = 3.38 ; ;

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{ 10**2-14**2-23**2 }{ 2 * 14 * 23 } ) = 13° 57'8" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-10**2-23**2 }{ 2 * 10 * 23 } ) = 19° 43'42" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-10**2-14**2 }{ 2 * 14 * 10 } ) = 146° 19'10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 38.82 }{ 23.5 } = 1.65 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 13° 57'8" } = 20.74 ; ;




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