14 18 29 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 18   c = 29

Area: T = 97.13987538524
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 21.8550073012° = 21°51' = 0.38113557159 rad
Angle ∠ B = β = 28.58985262968° = 28°35'19″ = 0.49989639122 rad
Angle ∠ C = γ = 129.5611400691° = 129°33'41″ = 2.26112730256 rad

Height: ha = 13.87769648361
Height: hb = 10.79331948725
Height: hc = 6.69992244036

Median: ma = 23.09876189249
Median: mb = 20.91765006634
Median: mc = 7.05333679898

Inradius: r = 3.18548771755
Circumradius: R = 18.80881473927

Vertex coordinates: A[29; 0] B[0; 0] C[12.29331034483; 6.69992244036]
Centroid: CG[13.76443678161; 2.23330748012]
Coordinates of the circumscribed circle: U[14.5; -11.9798998637]
Coordinates of the inscribed circle: I[12.5; 3.18548771755]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.1549926988° = 158°9' = 0.38113557159 rad
∠ B' = β' = 151.4111473703° = 151°24'41″ = 0.49989639122 rad
∠ C' = γ' = 50.43985993088° = 50°26'19″ = 2.26112730256 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 = 18 ; ; c = 29 ; ;

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

p = a+b+c = 14+18+29 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-14)(30.5-18)(30.5-29) } ; ; T = sqrt{ 9435.94 } = 97.14 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 97.14 }{ 14 } = 13.88 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 97.14 }{ 18 } = 10.79 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 97.14 }{ 29 } = 6.7 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 18**2+29**2-14**2 }{ 2 * 18 * 29 } ) = 21° 51' ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 14**2+29**2-18**2 }{ 2 * 14 * 29 } ) = 28° 35'19" ; ; gamma = 180° - alpha - beta = 180° - 21° 51' - 28° 35'19" = 129° 33'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 97.14 }{ 30.5 } = 3.18 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 14 }{ 2 * sin 21° 51' } = 18.81 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 18**2+2 * 29**2 - 14**2 } }{ 2 } = 23.098 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 29**2+2 * 14**2 - 18**2 } }{ 2 } = 20.917 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 18**2+2 * 14**2 - 29**2 } }{ 2 } = 7.053 ; ;
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