12 12 19 triangle

Obtuse isosceles triangle.

Sides: a = 12   b = 12   c = 19

Area: T = 69.64986719184
Perimeter: p = 43
Semiperimeter: s = 21.5

Angle ∠ A = α = 37.65884620062° = 37°39'30″ = 0.65772641532 rad
Angle ∠ B = β = 37.65884620062° = 37°39'30″ = 0.65772641532 rad
Angle ∠ C = γ = 104.6833075988° = 104°40'59″ = 1.82770643471 rad

Height: ha = 11.60881119864
Height: hb = 11.60881119864
Height: hc = 7.33114391493

Median: ma = 14.71439389696
Median: mb = 14.71439389696
Median: mc = 7.33114391493

Inradius: r = 3.23994731125
Circumradius: R = 9.82107184884

Vertex coordinates: A[19; 0] B[0; 0] C[9.5; 7.33114391493]
Centroid: CG[9.5; 2.44438130498]
Coordinates of the circumscribed circle: U[9.5; -2.48992793391]
Coordinates of the inscribed circle: I[9.5; 3.23994731125]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.3421537994° = 142°20'30″ = 0.65772641532 rad
∠ B' = β' = 142.3421537994° = 142°20'30″ = 0.65772641532 rad
∠ C' = γ' = 75.31769240124° = 75°19'1″ = 1.82770643471 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 = 12 ; ; c = 19 ; ;

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

p = a+b+c = 12+12+19 = 43 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 43 }{ 2 } = 21.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21.5 * (21.5-12)(21.5-12)(21.5-19) } ; ; T = sqrt{ 4850.94 } = 69.65 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 69.65 }{ 12 } = 11.61 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 69.65 }{ 12 } = 11.61 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 69.65 }{ 19 } = 7.33 ; ;

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**2-12**2-19**2 }{ 2 * 12 * 19 } ) = 37° 39'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-12**2-19**2 }{ 2 * 12 * 19 } ) = 37° 39'30" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-12**2-12**2 }{ 2 * 12 * 12 } ) = 104° 40'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 69.65 }{ 21.5 } = 3.24 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 37° 39'30" } = 9.82 ; ;




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