18 20 29 triangle

Obtuse scalene triangle.

Sides: a = 18   b = 20   c = 29

Area: T = 177.6087537847
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 37.76661251952° = 37°45'58″ = 0.65991432304 rad
Angle ∠ B = β = 42.88218397473° = 42°52'55″ = 0.74884292929 rad
Angle ∠ C = γ = 99.35220350576° = 99°21'7″ = 1.73440201303 rad

Height: ha = 19.73441708719
Height: hb = 17.76107537847
Height: hc = 12.24987957136

Median: ma = 23.22771392987
Median: mb = 21.96658826365
Median: mc = 12.31986849948

Inradius: r = 5.30217175477
Circumradius: R = 14.69553222349

Vertex coordinates: A[29; 0] B[0; 0] C[13.19896551724; 12.24987957136]
Centroid: CG[14.06332183908; 4.08329319045]
Coordinates of the circumscribed circle: U[14.5; -2.38879898632]
Coordinates of the inscribed circle: I[13.5; 5.30217175477]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.2343874805° = 142°14'2″ = 0.65991432304 rad
∠ B' = β' = 137.1188160253° = 137°7'5″ = 0.74884292929 rad
∠ C' = γ' = 80.64879649424° = 80°38'53″ = 1.73440201303 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 = 18 ; ; b = 20 ; ; c = 29 ; ;

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

p = a+b+c = 18+20+29 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-18)(33.5-20)(33.5-29) } ; ; T = sqrt{ 31544.44 } = 177.61 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 177.61 }{ 18 } = 19.73 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 177.61 }{ 20 } = 17.76 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 177.61 }{ 29 } = 12.25 ; ;

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{ 18**2-20**2-29**2 }{ 2 * 20 * 29 } ) = 37° 45'58" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-18**2-29**2 }{ 2 * 18 * 29 } ) = 42° 52'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-18**2-20**2 }{ 2 * 20 * 18 } ) = 99° 21'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 177.61 }{ 33.5 } = 5.3 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 37° 45'58" } = 14.7 ; ;




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