19 29 29 triangle

Acute isosceles triangle.

Sides: a = 19   b = 29   c = 29

Area: T = 260.2988266418
Perimeter: p = 77
Semiperimeter: s = 38.5

Angle ∠ A = α = 38.24546667831° = 38°14'41″ = 0.66774953567 rad
Angle ∠ B = β = 70.87876666085° = 70°52'40″ = 1.23770486484 rad
Angle ∠ C = γ = 70.87876666085° = 70°52'40″ = 1.23770486484 rad

Height: ha = 27.43998175176
Height: hb = 17.95216045805
Height: hc = 17.95216045805

Median: ma = 27.43998175176
Median: mb = 19.76773974008
Median: mc = 19.76773974008

Inradius: r = 6.76109939329
Circumradius: R = 15.34768175374

Vertex coordinates: A[29; 0] B[0; 0] C[6.2244137931; 17.95216045805]
Centroid: CG[11.74113793103; 5.98438681935]
Coordinates of the circumscribed circle: U[14.5; 5.0277405745]
Coordinates of the inscribed circle: I[9.5; 6.76109939329]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.7555333217° = 141°45'19″ = 0.66774953567 rad
∠ B' = β' = 109.1222333392° = 109°7'20″ = 1.23770486484 rad
∠ C' = γ' = 109.1222333392° = 109°7'20″ = 1.23770486484 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 = 29 ; ; c = 29 ; ;

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

p = a+b+c = 19+29+29 = 77 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 77 }{ 2 } = 38.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 38.5 * (38.5-19)(38.5-29)(38.5-29) } ; ; T = sqrt{ 67755.19 } = 260.3 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 260.3 }{ 19 } = 27.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 260.3 }{ 29 } = 17.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 260.3 }{ 29 } = 17.95 ; ;

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**2-29**2-29**2 }{ 2 * 29 * 29 } ) = 38° 14'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-19**2-29**2 }{ 2 * 19 * 29 } ) = 70° 52'40" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-19**2-29**2 }{ 2 * 29 * 19 } ) = 70° 52'40" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 260.3 }{ 38.5 } = 6.76 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 38° 14'41" } = 15.35 ; ;




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