14 17 29 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 17   c = 29

Area: T = 78.99436706325
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 18.69108148701° = 18°41'27″ = 0.32662162594 rad
Angle ∠ B = β = 22.99004622732° = 22°54'2″ = 0.43996884669 rad
Angle ∠ C = γ = 138.4098722857° = 138°24'31″ = 2.41656879273 rad

Height: ha = 11.28548100904
Height: hb = 9.29333730156
Height: hc = 5.4487839354

Median: ma = 22.71656333832
Median: mb = 21.12546301743
Median: mc = 5.67989083458

Inradius: r = 2.63331223544
Circumradius: R = 21.84435222238

Vertex coordinates: A[29; 0] B[0; 0] C[12.89765517241; 5.4487839354]
Centroid: CG[13.96655172414; 1.81659464513]
Coordinates of the circumscribed circle: U[14.5; -16.33767519153]
Coordinates of the inscribed circle: I[13; 2.63331223544]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.309918513° = 161°18'33″ = 0.32662162594 rad
∠ B' = β' = 157.1099537727° = 157°5'58″ = 0.43996884669 rad
∠ C' = γ' = 41.59112771434° = 41°35'29″ = 2.41656879273 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 = 17 ; ; c = 29 ; ;

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

p = a+b+c = 14+17+29 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-14)(30-17)(30-29) } ; ; T = sqrt{ 6240 } = 78.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 78.99 }{ 14 } = 11.28 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 78.99 }{ 17 } = 9.29 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 78.99 }{ 29 } = 5.45 ; ;

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**2-17**2-29**2 }{ 2 * 17 * 29 } ) = 18° 41'27" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-14**2-29**2 }{ 2 * 14 * 29 } ) = 22° 54'2" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-14**2-17**2 }{ 2 * 17 * 14 } ) = 138° 24'31" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 78.99 }{ 30 } = 2.63 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 18° 41'27" } = 21.84 ; ;




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