13 18 29 triangle

Obtuse scalene triangle.

Sides: a = 13   b = 18   c = 29

Area: T = 78.23304288624
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 17.44215938563° = 17°26'30″ = 0.30444132396 rad
Angle ∠ B = β = 24.5220294972° = 24°31'13″ = 0.42879598808 rad
Angle ∠ C = γ = 138.0388111172° = 138°2'17″ = 2.40992195332 rad

Height: ha = 12.03554505942
Height: hb = 8.69222698736
Height: hc = 5.39552019905

Median: ma = 23.24332785983
Median: mb = 20.5911260282
Median: mc = 6.02107972894

Inradius: r = 2.60876809621
Circumradius: R = 21.68659350597

Vertex coordinates: A[29; 0] B[0; 0] C[11.82875862069; 5.39552019905]
Centroid: CG[13.60991954023; 1.79884006635]
Coordinates of the circumscribed circle: U[14.5; -16.12554388905]
Coordinates of the inscribed circle: I[12; 2.60876809621]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.5588406144° = 162°33'30″ = 0.30444132396 rad
∠ B' = β' = 155.4879705028° = 155°28'47″ = 0.42879598808 rad
∠ C' = γ' = 41.96218888284° = 41°57'43″ = 2.40992195332 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 = 13 ; ; b = 18 ; ; c = 29 ; ;

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

p = a+b+c = 13+18+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 * (30-13)(30-18)(30-29) } ; ; T = sqrt{ 6120 } = 78.23 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 78.23 }{ 13 } = 12.04 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 78.23 }{ 18 } = 8.69 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 78.23 }{ 29 } = 5.4 ; ;

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{ 13**2-18**2-29**2 }{ 2 * 18 * 29 } ) = 17° 26'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-13**2-29**2 }{ 2 * 13 * 29 } ) = 24° 31'13" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-13**2-18**2 }{ 2 * 18 * 13 } ) = 138° 2'17" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 78.23 }{ 30 } = 2.61 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 17° 26'30" } = 21.69 ; ;




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