12 18 29 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 18   c = 29

Area: T = 54.48333690221
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 12.04990235938° = 12°2'56″ = 0.21102951334 rad
Angle ∠ B = β = 18.24875267096° = 18°14'51″ = 0.31884794214 rad
Angle ∠ C = γ = 149.7033449697° = 149°42'12″ = 2.61328180988 rad

Height: ha = 9.08105615037
Height: hb = 6.05437076691
Height: hc = 3.75774737257

Median: ma = 23.37773394551
Median: mb = 20.28554627751
Median: mc = 4.87333971724

Inradius: r = 1.84768938652
Circumradius: R = 28.74327159536

Vertex coordinates: A[29; 0] B[0; 0] C[11.39765517241; 3.75774737257]
Centroid: CG[13.46655172414; 1.25224912419]
Coordinates of the circumscribed circle: U[14.5; -24.81772061359]
Coordinates of the inscribed circle: I[11.5; 1.84768938652]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.9510976406° = 167°57'4″ = 0.21102951334 rad
∠ B' = β' = 161.752247329° = 161°45'9″ = 0.31884794214 rad
∠ C' = γ' = 30.29765503033° = 30°17'48″ = 2.61328180988 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 = 12 ; ; b = 18 ; ; c = 29 ; ;

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

p = a+b+c = 12+18+29 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-12)(29.5-18)(29.5-29) } ; ; T = sqrt{ 2968.44 } = 54.48 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 54.48 }{ 12 } = 9.08 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 54.48 }{ 18 } = 6.05 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 54.48 }{ 29 } = 3.76 ; ;

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{ 12**2-18**2-29**2 }{ 2 * 18 * 29 } ) = 12° 2'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-12**2-29**2 }{ 2 * 12 * 29 } ) = 18° 14'51" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-12**2-18**2 }{ 2 * 18 * 12 } ) = 149° 42'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 54.48 }{ 29.5 } = 1.85 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 12° 2'56" } = 28.74 ; ;




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