16 18 23 triangle

Acute scalene triangle.

Sides: a = 16   b = 18   c = 23

Area: T = 143.4344436242
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 43.86216975242° = 43°51'42″ = 0.76655310373 rad
Angle ∠ B = β = 51.21880182686° = 51°13'5″ = 0.89439230551 rad
Angle ∠ C = γ = 84.92202842073° = 84°55'13″ = 1.48221385611 rad

Height: ha = 17.92993045302
Height: hb = 15.93771595824
Height: hc = 12.47325596732

Median: ma = 19.03994327647
Median: mb = 17.64993625947
Median: mc = 12.56598566871

Inradius: r = 5.03327872366
Circumradius: R = 11.54553446424

Vertex coordinates: A[23; 0] B[0; 0] C[10.02217391304; 12.47325596732]
Centroid: CG[11.00772463768; 4.15875198911]
Coordinates of the circumscribed circle: U[11.5; 1.02222440569]
Coordinates of the inscribed circle: I[10.5; 5.03327872366]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 136.1388302476° = 136°8'18″ = 0.76655310373 rad
∠ B' = β' = 128.7821981731° = 128°46'55″ = 0.89439230551 rad
∠ C' = γ' = 95.08797157927° = 95°4'47″ = 1.48221385611 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 = 16 ; ; b = 18 ; ; c = 23 ; ;

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

p = a+b+c = 16+18+23 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-16)(28.5-18)(28.5-23) } ; ; T = sqrt{ 20573.44 } = 143.43 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 143.43 }{ 16 } = 17.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 143.43 }{ 18 } = 15.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 143.43 }{ 23 } = 12.47 ; ;

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{ 16**2-18**2-23**2 }{ 2 * 18 * 23 } ) = 43° 51'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-16**2-23**2 }{ 2 * 16 * 23 } ) = 51° 13'5" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-16**2-18**2 }{ 2 * 18 * 16 } ) = 84° 55'13" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 143.43 }{ 28.5 } = 5.03 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 43° 51'42" } = 11.55 ; ;




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