19 19 30 triangle

Obtuse isosceles triangle.

Sides: a = 19   b = 19   c = 30

Area: T = 174.9298556845
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 37.86436463617° = 37°51'49″ = 0.66108452958 rad
Angle ∠ B = β = 37.86436463617° = 37°51'49″ = 0.66108452958 rad
Angle ∠ C = γ = 104.2732707277° = 104°16'22″ = 1.82199020619 rad

Height: ha = 18.41435322995
Height: hb = 18.41435322995
Height: hc = 11.66219037897

Median: ma = 23.24332785983
Median: mb = 23.24332785983
Median: mc = 11.66219037897

Inradius: r = 5.14549575543
Circumradius: R = 15.47877473091

Vertex coordinates: A[30; 0] B[0; 0] C[15; 11.66219037897]
Centroid: CG[15; 3.88773012632]
Coordinates of the circumscribed circle: U[15; -3.81658435194]
Coordinates of the inscribed circle: I[15; 5.14549575543]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.1366353638° = 142°8'11″ = 0.66108452958 rad
∠ B' = β' = 142.1366353638° = 142°8'11″ = 0.66108452958 rad
∠ C' = γ' = 75.72772927235° = 75°43'38″ = 1.82199020619 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 = 19 ; ; b = 19 ; ; c = 30 ; ;

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

p = a+b+c = 19+19+30 = 68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 68 }{ 2 } = 34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34 * (34-19)(34-19)(34-30) } ; ; T = sqrt{ 30600 } = 174.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 174.93 }{ 19 } = 18.41 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 174.93 }{ 19 } = 18.41 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 174.93 }{ 30 } = 11.66 ; ;

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{ 19**2-19**2-30**2 }{ 2 * 19 * 30 } ) = 37° 51'49" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-19**2-30**2 }{ 2 * 19 * 30 } ) = 37° 51'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-19**2-19**2 }{ 2 * 19 * 19 } ) = 104° 16'22" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 174.93 }{ 34 } = 5.14 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 37° 51'49" } = 15.48 ; ;




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