12 25 29 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 25   c = 29

Area: T = 148.9166083752
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 24.25552873422° = 24°15'19″ = 0.42333346251 rad
Angle ∠ B = β = 58.85326100785° = 58°51'9″ = 1.02771718193 rad
Angle ∠ C = γ = 96.89221025793° = 96°53'32″ = 1.69110862092 rad

Height: ha = 24.8199347292
Height: hb = 11.91332867002
Height: hc = 10.27700747415

Median: ma = 26.40107575649
Median: mb = 18.33771208209
Median: mc = 13.22003787824

Inradius: r = 4.51326085985
Circumradius: R = 14.6065541223

Vertex coordinates: A[29; 0] B[0; 0] C[6.20768965517; 10.27700747415]
Centroid: CG[11.73656321839; 3.42333582472]
Coordinates of the circumscribed circle: U[14.5; -1.75326649468]
Coordinates of the inscribed circle: I[8; 4.51326085985]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.7454712658° = 155°44'41″ = 0.42333346251 rad
∠ B' = β' = 121.1477389922° = 121°8'51″ = 1.02771718193 rad
∠ C' = γ' = 83.10878974207° = 83°6'28″ = 1.69110862092 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 = 25 ; ; c = 29 ; ;

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

p = a+b+c = 12+25+29 = 66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 66 }{ 2 } = 33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33 * (33-12)(33-25)(33-29) } ; ; T = sqrt{ 22176 } = 148.92 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 148.92 }{ 12 } = 24.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 148.92 }{ 25 } = 11.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 148.92 }{ 29 } = 10.27 ; ;

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**2-25**2-29**2 }{ 2 * 25 * 29 } ) = 24° 15'19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-12**2-29**2 }{ 2 * 12 * 29 } ) = 58° 51'9" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-12**2-25**2 }{ 2 * 25 * 12 } ) = 96° 53'32" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 148.92 }{ 33 } = 4.51 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 24° 15'19" } = 14.61 ; ;




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