16 19 19 triangle

Acute isosceles triangle.

Sides: a = 16   b = 19   c = 19

Area: T = 137.8769503517
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 49.80221247407° = 49°48'8″ = 0.86992110512 rad
Angle ∠ B = β = 65.09989376296° = 65°5'56″ = 1.13661908012 rad
Angle ∠ C = γ = 65.09989376296° = 65°5'56″ = 1.13661908012 rad

Height: ha = 17.23436879396
Height: hb = 14.51325793176
Height: hc = 14.51325793176

Median: ma = 17.23436879396
Median: mb = 14.77332867027
Median: mc = 14.77332867027

Inradius: r = 5.1066277908
Circumradius: R = 10.47436723

Vertex coordinates: A[19; 0] B[0; 0] C[6.73768421053; 14.51325793176]
Centroid: CG[8.57989473684; 4.83875264392]
Coordinates of the circumscribed circle: U[9.5; 4.41099672842]
Coordinates of the inscribed circle: I[8; 5.1066277908]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.1987875259° = 130°11'52″ = 0.86992110512 rad
∠ B' = β' = 114.901106237° = 114°54'4″ = 1.13661908012 rad
∠ C' = γ' = 114.901106237° = 114°54'4″ = 1.13661908012 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 = 19 ; ; c = 19 ; ;

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

p = a+b+c = 16+19+19 = 54 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 54 }{ 2 } = 27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27 * (27-16)(27-19)(27-19) } ; ; T = sqrt{ 19008 } = 137.87 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 137.87 }{ 16 } = 17.23 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 137.87 }{ 19 } = 14.51 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 137.87 }{ 19 } = 14.51 ; ;

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**2-19**2-19**2 }{ 2 * 19 * 19 } ) = 49° 48'8" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-16**2-19**2 }{ 2 * 16 * 19 } ) = 65° 5'56" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-16**2-19**2 }{ 2 * 19 * 16 } ) = 65° 5'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 137.87 }{ 27 } = 5.11 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 49° 48'8" } = 10.47 ; ;




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