12 19 19 triangle

Acute isosceles triangle.

Sides: a = 12   b = 19   c = 19

Area: T = 108.1676538264
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 36.81769603412° = 36°49'1″ = 0.64325771785 rad
Angle ∠ B = β = 71.59215198294° = 71°35'29″ = 1.25495077375 rad
Angle ∠ C = γ = 71.59215198294° = 71°35'29″ = 1.25495077375 rad

Height: ha = 18.02877563773
Height: hb = 11.38659513962
Height: hc = 11.38659513962

Median: ma = 18.02877563773
Median: mb = 12.73877392029
Median: mc = 12.73877392029

Inradius: r = 4.32766615306
Circumradius: R = 10.01223385419

Vertex coordinates: A[19; 0] B[0; 0] C[3.78994736842; 11.38659513962]
Centroid: CG[7.59664912281; 3.79553171321]
Coordinates of the circumscribed circle: U[9.5; 3.16217911185]
Coordinates of the inscribed circle: I[6; 4.32766615306]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.1833039659° = 143°10'59″ = 0.64325771785 rad
∠ B' = β' = 108.4088480171° = 108°24'31″ = 1.25495077375 rad
∠ C' = γ' = 108.4088480171° = 108°24'31″ = 1.25495077375 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 = 12 ; ; b = 19 ; ; c = 19 ; ;

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

p = a+b+c = 12+19+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 * (25-12)(25-19)(25-19) } ; ; T = sqrt{ 11700 } = 108.17 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 108.17 }{ 12 } = 18.03 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 108.17 }{ 19 } = 11.39 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 108.17 }{ 19 } = 11.39 ; ;

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{ 12**2-19**2-19**2 }{ 2 * 19 * 19 } ) = 36° 49'1" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-12**2-19**2 }{ 2 * 12 * 19 } ) = 71° 35'29" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-12**2-19**2 }{ 2 * 19 * 12 } ) = 71° 35'29" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 108.17 }{ 25 } = 4.33 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 36° 49'1" } = 10.01 ; ;




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