19 20 29 triangle

Obtuse scalene triangle.

Sides: a = 19   b = 20   c = 29

Area: T = 188.9444436277
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 40.6577248638° = 40°39'26″ = 0.71096028535 rad
Angle ∠ B = β = 43.33004229429° = 43°18'2″ = 0.75657349479 rad
Angle ∠ C = γ = 96.04223284191° = 96°2'32″ = 1.67662548522 rad

Height: ha = 19.88988880291
Height: hb = 18.89444436277
Height: hc = 13.03106507777

Median: ma = 23.02771578793
Median: mb = 22.38330292856
Median: mc = 13.04879883507

Inradius: r = 5.55771893023
Circumradius: R = 14.58110062169

Vertex coordinates: A[29; 0] B[0; 0] C[13.82875862069; 13.03106507777]
Centroid: CG[14.2765862069; 4.34435502592]
Coordinates of the circumscribed circle: U[14.5; -1.53548427597]
Coordinates of the inscribed circle: I[14; 5.55771893023]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.3432751362° = 139°20'34″ = 0.71096028535 rad
∠ B' = β' = 136.7699577057° = 136°41'58″ = 0.75657349479 rad
∠ C' = γ' = 83.95876715809° = 83°57'28″ = 1.67662548522 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 = 20 ; ; c = 29 ; ;

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

p = a+b+c = 19+20+29 = 68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 68 }{ 2 } = 34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34 * (34-19)(34-20)(34-29) } ; ; T = sqrt{ 35700 } = 188.94 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 188.94 }{ 19 } = 19.89 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 188.94 }{ 20 } = 18.89 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 188.94 }{ 29 } = 13.03 ; ;

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**2-20**2-29**2 }{ 2 * 20 * 29 } ) = 40° 39'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-19**2-29**2 }{ 2 * 19 * 29 } ) = 43° 18'2" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-19**2-20**2 }{ 2 * 20 * 19 } ) = 96° 2'32" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 188.94 }{ 34 } = 5.56 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 40° 39'26" } = 14.58 ; ;




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