14 16 23 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 16   c = 23

Area: T = 110.3333301863
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 36.84439406298° = 36°50'38″ = 0.64330480734 rad
Angle ∠ B = β = 43.25992059274° = 43°15'33″ = 0.75550155752 rad
Angle ∠ C = γ = 99.89768534428° = 99°53'49″ = 1.7443529005 rad

Height: ha = 15.76219002661
Height: hb = 13.79216627329
Height: hc = 9.5944200162

Median: ma = 18.53437529929
Median: mb = 17.27771525432
Median: mc = 9.68224583655

Inradius: r = 4.1643520825
Circumradius: R = 11.67437193418

Vertex coordinates: A[23; 0] B[0; 0] C[10.19656521739; 9.5944200162]
Centroid: CG[11.06552173913; 3.19880667207]
Coordinates of the circumscribed circle: U[11.5; -2.00664205119]
Coordinates of the inscribed circle: I[10.5; 4.1643520825]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.156605937° = 143°9'22″ = 0.64330480734 rad
∠ B' = β' = 136.7410794073° = 136°44'27″ = 0.75550155752 rad
∠ C' = γ' = 80.10331465572° = 80°6'11″ = 1.7443529005 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 = 16 ; ; c = 23 ; ;

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

p = a+b+c = 14+16+23 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-14)(26.5-16)(26.5-23) } ; ; T = sqrt{ 12173.44 } = 110.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 110.33 }{ 14 } = 15.76 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 110.33 }{ 16 } = 13.79 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 110.33 }{ 23 } = 9.59 ; ;

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**2-16**2-23**2 }{ 2 * 16 * 23 } ) = 36° 50'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-14**2-23**2 }{ 2 * 14 * 23 } ) = 43° 15'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-14**2-16**2 }{ 2 * 16 * 14 } ) = 99° 53'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 110.33 }{ 26.5 } = 4.16 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 36° 50'38" } = 11.67 ; ;




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