14 18 19 triangle

Acute scalene triangle.

Sides: a = 14   b = 18   c = 19

Area: T = 119.5665620059
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 44.36439892911° = 44°21'50″ = 0.77442976824 rad
Angle ∠ B = β = 64.02655740731° = 64°1'32″ = 1.11774570731 rad
Angle ∠ C = γ = 71.61104366358° = 71°36'38″ = 1.25498378981 rad

Height: ha = 17.08108028655
Height: hb = 13.28550688954
Height: hc = 12.5865854743

Median: ma = 17.1321841699
Median: mb = 14.05334693226
Median: mc = 13.02988142208

Inradius: r = 4.68988478454
Circumradius: R = 10.01112390118

Vertex coordinates: A[19; 0] B[0; 0] C[6.13215789474; 12.5865854743]
Centroid: CG[8.37771929825; 4.19552849143]
Coordinates of the circumscribed circle: U[9.5; 3.15883075454]
Coordinates of the inscribed circle: I[7.5; 4.68988478454]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.6366010709° = 135°38'10″ = 0.77442976824 rad
∠ B' = β' = 115.9744425927° = 115°58'28″ = 1.11774570731 rad
∠ C' = γ' = 108.3989563364° = 108°23'22″ = 1.25498378981 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 = 18 ; ; c = 19 ; ;

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

p = a+b+c = 14+18+19 = 51 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 51 }{ 2 } = 25.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25.5 * (25.5-14)(25.5-18)(25.5-19) } ; ; T = sqrt{ 14295.94 } = 119.57 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 119.57 }{ 14 } = 17.08 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 119.57 }{ 18 } = 13.29 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 119.57 }{ 19 } = 12.59 ; ;

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**2-18**2-19**2 }{ 2 * 18 * 19 } ) = 44° 21'50" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-14**2-19**2 }{ 2 * 14 * 19 } ) = 64° 1'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-14**2-18**2 }{ 2 * 18 * 14 } ) = 71° 36'38" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 119.57 }{ 25.5 } = 4.69 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 44° 21'50" } = 10.01 ; ;




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