9 25 29 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 25   c = 29

Area: T = 107.3188160159
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 17.22105164629° = 17°13'14″ = 0.30105547112 rad
Angle ∠ B = β = 55.32218804133° = 55°19'19″ = 0.96655489616 rad
Angle ∠ C = γ = 107.4587603124° = 107°27'27″ = 1.87554889808 rad

Height: ha = 23.84884800354
Height: hb = 8.58554528128
Height: hc = 7.40112524248

Median: ma = 26.69773781484
Median: mb = 17.45770902501
Median: mc = 11.94878031453

Inradius: r = 3.40769257193
Circumradius: R = 15.22001301325

Vertex coordinates: A[29; 0] B[0; 0] C[5.12106896552; 7.40112524248]
Centroid: CG[11.37435632184; 2.46770841416]
Coordinates of the circumscribed circle: U[14.5; -4.56600390397]
Coordinates of the inscribed circle: I[6.5; 3.40769257193]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.7799483537° = 162°46'46″ = 0.30105547112 rad
∠ B' = β' = 124.6788119587° = 124°40'41″ = 0.96655489616 rad
∠ C' = γ' = 72.54223968763° = 72°32'33″ = 1.87554889808 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 = 9 ; ; b = 25 ; ; c = 29 ; ;

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

p = a+b+c = 9+25+29 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-9)(31.5-25)(31.5-29) } ; ; T = sqrt{ 11517.19 } = 107.32 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 107.32 }{ 9 } = 23.85 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 107.32 }{ 25 } = 8.59 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 107.32 }{ 29 } = 7.4 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 25**2+29**2-9**2 }{ 2 * 25 * 29 } ) = 17° 13'14" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 9**2+29**2-25**2 }{ 2 * 9 * 29 } ) = 55° 19'19" ; ; gamma = 180° - alpha - beta = 180° - 17° 13'14" - 55° 19'19" = 107° 27'27" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 107.32 }{ 31.5 } = 3.41 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 9 }{ 2 * sin 17° 13'14" } = 15.2 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 25**2+2 * 29**2 - 9**2 } }{ 2 } = 26.697 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 29**2+2 * 9**2 - 25**2 } }{ 2 } = 17.457 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 25**2+2 * 9**2 - 29**2 } }{ 2 } = 11.948 ; ;
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