5 28 29 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 28   c = 29

Area: T = 69.54113546029
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 9.86224891647° = 9°51'45″ = 0.17221329084 rad
Angle ∠ B = β = 73.57550829667° = 73°34'30″ = 1.28441274452 rad
Angle ∠ C = γ = 96.56224278686° = 96°33'45″ = 1.68553323 rad

Height: ha = 27.81765418411
Height: hb = 4.96772396145
Height: hc = 4.79659554899

Median: ma = 28.3954541729
Median: mb = 15.39548043183
Median: mc = 13.93773598648

Inradius: r = 2.24332695033
Circumradius: R = 14.59656317043

Vertex coordinates: A[29; 0] B[0; 0] C[1.41437931034; 4.79659554899]
Centroid: CG[10.13879310345; 1.599865183]
Coordinates of the circumscribed circle: U[14.5; -1.66880721948]
Coordinates of the inscribed circle: I[3; 2.24332695033]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.1387510835° = 170°8'15″ = 0.17221329084 rad
∠ B' = β' = 106.4254917033° = 106°25'30″ = 1.28441274452 rad
∠ C' = γ' = 83.43875721314° = 83°26'15″ = 1.68553323 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 = 5 ; ; b = 28 ; ; c = 29 ; ;

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

p = a+b+c = 5+28+29 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-5)(31-28)(31-29) } ; ; T = sqrt{ 4836 } = 69.54 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 69.54 }{ 5 } = 27.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 69.54 }{ 28 } = 4.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 69.54 }{ 29 } = 4.8 ; ;

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{ 5**2-28**2-29**2 }{ 2 * 28 * 29 } ) = 9° 51'45" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-5**2-29**2 }{ 2 * 5 * 29 } ) = 73° 34'30" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-5**2-28**2 }{ 2 * 28 * 5 } ) = 96° 33'45" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 69.54 }{ 31 } = 2.24 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 9° 51'45" } = 14.6 ; ;




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