19 25 29 triangle

Acute scalene triangle.

Sides: a = 19   b = 25   c = 29

Area: T = 234.7177250112
Perimeter: p = 73
Semiperimeter: s = 36.5

Angle ∠ A = α = 40.35330656205° = 40°21'11″ = 0.70442938584 rad
Angle ∠ B = β = 58.42663957187° = 58°25'35″ = 1.02197329754 rad
Angle ∠ C = γ = 81.22105386608° = 81°13'14″ = 1.41875658199 rad

Height: ha = 24.70770789591
Height: hb = 18.77773800089
Height: hc = 16.18773965594

Median: ma = 25.35325146682
Median: mb = 21.0899096709
Median: mc = 16.81551717208

Inradius: r = 6.43106095921
Circumradius: R = 14.67219084275

Vertex coordinates: A[29; 0] B[0; 0] C[9.94882758621; 16.18773965594]
Centroid: CG[12.98327586207; 5.39657988531]
Coordinates of the circumscribed circle: U[14.5; 2.23993965495]
Coordinates of the inscribed circle: I[11.5; 6.43106095921]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.6476934379° = 139°38'49″ = 0.70442938584 rad
∠ B' = β' = 121.5743604281° = 121°34'25″ = 1.02197329754 rad
∠ C' = γ' = 98.77994613392° = 98°46'46″ = 1.41875658199 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 = 25 ; ; c = 29 ; ;

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

p = a+b+c = 19+25+29 = 73 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 73 }{ 2 } = 36.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36.5 * (36.5-19)(36.5-25)(36.5-29) } ; ; T = sqrt{ 55092.19 } = 234.72 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 234.72 }{ 19 } = 24.71 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 234.72 }{ 25 } = 18.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 234.72 }{ 29 } = 16.19 ; ;

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**2-25**2-29**2 }{ 2 * 25 * 29 } ) = 40° 21'11" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-19**2-29**2 }{ 2 * 19 * 29 } ) = 58° 25'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-19**2-25**2 }{ 2 * 25 * 19 } ) = 81° 13'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 234.72 }{ 36.5 } = 6.43 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 40° 21'11" } = 14.67 ; ;




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