14 17 19 triangle

Acute scalene triangle.

Sides: a = 14   b = 17   c = 19

Area: T = 114.8911252931
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 45.3499014834° = 45°20'56″ = 0.79114896214 rad
Angle ∠ B = β = 59.75109669494° = 59°45'3″ = 1.04328511045 rad
Angle ∠ C = γ = 74.99000182166° = 74°54' = 1.30772519277 rad

Height: ha = 16.4133036133
Height: hb = 13.51766179919
Height: hc = 12.0943816098

Median: ma = 16.61332477258
Median: mb = 14.36114066163
Median: mc = 12.33989626793

Inradius: r = 4.59656501172
Circumradius: R = 9.84397395029

Vertex coordinates: A[19; 0] B[0; 0] C[7.05326315789; 12.0943816098]
Centroid: CG[8.68442105263; 4.03112720327]
Coordinates of the circumscribed circle: U[9.5; 2.56332934839]
Coordinates of the inscribed circle: I[8; 4.59656501172]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.6510985166° = 134°39'4″ = 0.79114896214 rad
∠ B' = β' = 120.2499033051° = 120°14'57″ = 1.04328511045 rad
∠ C' = γ' = 105.1099981783° = 105°6' = 1.30772519277 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 = 17 ; ; c = 19 ; ;

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

p = a+b+c = 14+17+19 = 50 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 50 }{ 2 } = 25 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25 * (25-14)(25-17)(25-19) } ; ; T = sqrt{ 13200 } = 114.89 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 114.89 }{ 14 } = 16.41 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 114.89 }{ 17 } = 13.52 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 114.89 }{ 19 } = 12.09 ; ;

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**2-17**2-19**2 }{ 2 * 17 * 19 } ) = 45° 20'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-14**2-19**2 }{ 2 * 14 * 19 } ) = 59° 45'3" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-14**2-17**2 }{ 2 * 17 * 14 } ) = 74° 54' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 114.89 }{ 25 } = 4.6 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 45° 20'56" } = 9.84 ; ;




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