19 30 30 triangle

Acute isosceles triangle.

Sides: a = 19   b = 30   c = 30

Area: T = 270.3333012227
Perimeter: p = 79
Semiperimeter: s = 39.5

Angle ∠ A = α = 36.92329165935° = 36°55'23″ = 0.6444426464 rad
Angle ∠ B = β = 71.53985417032° = 71°32'19″ = 1.24985830948 rad
Angle ∠ C = γ = 71.53985417032° = 71°32'19″ = 1.24985830948 rad

Height: ha = 28.45661065503
Height: hb = 18.02222008152
Height: hc = 18.02222008152

Median: ma = 28.45661065503
Median: mb = 20.13770305656
Median: mc = 20.13770305656

Inradius: r = 6.84438737273
Circumradius: R = 15.81438288949

Vertex coordinates: A[30; 0] B[0; 0] C[6.01766666667; 18.02222008152]
Centroid: CG[12.00655555556; 6.00774002717]
Coordinates of the circumscribed circle: U[15; 5.00877124834]
Coordinates of the inscribed circle: I[9.5; 6.84438737273]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.0777083406° = 143°4'37″ = 0.6444426464 rad
∠ B' = β' = 108.4611458297° = 108°27'41″ = 1.24985830948 rad
∠ C' = γ' = 108.4611458297° = 108°27'41″ = 1.24985830948 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 = 30 ; ; c = 30 ; ;

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

p = a+b+c = 19+30+30 = 79 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 79 }{ 2 } = 39.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 39.5 * (39.5-19)(39.5-30)(39.5-30) } ; ; T = sqrt{ 73079.94 } = 270.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 270.33 }{ 19 } = 28.46 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 270.33 }{ 30 } = 18.02 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 270.33 }{ 30 } = 18.02 ; ;

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**2-30**2-30**2 }{ 2 * 30 * 30 } ) = 36° 55'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 30**2-19**2-30**2 }{ 2 * 19 * 30 } ) = 71° 32'19" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-19**2-30**2 }{ 2 * 30 * 19 } ) = 71° 32'19" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 270.33 }{ 39.5 } = 6.84 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 36° 55'23" } = 15.81 ; ;




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