16 16 19 triangle

Acute isosceles triangle.

Sides: a = 16   b = 16   c = 19

Area: T = 122.3076735301
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 53.57664263577° = 53°34'35″ = 0.93550850414 rad
Angle ∠ B = β = 53.57664263577° = 53°34'35″ = 0.93550850414 rad
Angle ∠ C = γ = 72.84771472847° = 72°50'50″ = 1.27114225708 rad

Height: ha = 15.28883419126
Height: hb = 15.28883419126
Height: hc = 12.87443931896

Median: ma = 15.63664957711
Median: mb = 15.63664957711
Median: mc = 12.87443931896

Inradius: r = 4.79663425608
Circumradius: R = 9.94222161585

Vertex coordinates: A[19; 0] B[0; 0] C[9.5; 12.87443931896]
Centroid: CG[9.5; 4.29114643965]
Coordinates of the circumscribed circle: U[9.5; 2.93221770311]
Coordinates of the inscribed circle: I[9.5; 4.79663425608]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 126.4243573642° = 126°25'25″ = 0.93550850414 rad
∠ B' = β' = 126.4243573642° = 126°25'25″ = 0.93550850414 rad
∠ C' = γ' = 107.1532852715° = 107°9'10″ = 1.27114225708 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 = 16 ; ; c = 19 ; ;

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

p = a+b+c = 16+16+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 * (25.5-16)(25.5-16)(25.5-19) } ; ; T = sqrt{ 14958.94 } = 122.31 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 122.31 }{ 16 } = 15.29 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 122.31 }{ 16 } = 15.29 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 122.31 }{ 19 } = 12.87 ; ;

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**2-16**2-19**2 }{ 2 * 16 * 19 } ) = 53° 34'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-16**2-19**2 }{ 2 * 16 * 19 } ) = 53° 34'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-16**2-16**2 }{ 2 * 16 * 16 } ) = 72° 50'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 122.31 }{ 25.5 } = 4.8 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 53° 34'35" } = 9.94 ; ;




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