14 19 19 triangle

Acute isosceles triangle.

Sides: a = 14   b = 19   c = 19

Area: T = 123.6454652129
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 43.23765448443° = 43°14'12″ = 0.75546200647 rad
Angle ∠ B = β = 68.38217275778° = 68°22'54″ = 1.19334862944 rad
Angle ∠ C = γ = 68.38217275778° = 68°22'54″ = 1.19334862944 rad

Height: ha = 17.66435217327
Height: hb = 13.01552265399
Height: hc = 13.01552265399

Median: ma = 17.66435217327
Median: mb = 13.7220422734
Median: mc = 13.7220422734

Inradius: r = 4.75655635434
Circumradius: R = 10.21988002332

Vertex coordinates: A[19; 0] B[0; 0] C[5.15878947368; 13.01552265399]
Centroid: CG[8.05326315789; 4.33884088466]
Coordinates of the circumscribed circle: U[9.5; 3.76548211385]
Coordinates of the inscribed circle: I[7; 4.75655635434]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 136.7633455156° = 136°45'48″ = 0.75546200647 rad
∠ B' = β' = 111.6188272422° = 111°37'6″ = 1.19334862944 rad
∠ C' = γ' = 111.6188272422° = 111°37'6″ = 1.19334862944 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 = 14 ; ; b = 19 ; ; c = 19 ; ;

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

p = a+b+c = 14+19+19 = 52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 52 }{ 2 } = 26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26 * (26-14)(26-19)(26-19) } ; ; T = sqrt{ 15288 } = 123.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 123.64 }{ 14 } = 17.66 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 123.64 }{ 19 } = 13.02 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 123.64 }{ 19 } = 13.02 ; ;

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{ 14**2-19**2-19**2 }{ 2 * 19 * 19 } ) = 43° 14'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-14**2-19**2 }{ 2 * 14 * 19 } ) = 68° 22'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-14**2-19**2 }{ 2 * 19 * 14 } ) = 68° 22'54" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 123.64 }{ 26 } = 4.76 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 43° 14'12" } = 10.22 ; ;




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