10 24 29 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 24   c = 29

Area: T = 112.687734401
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 18.89437495493° = 18°53'37″ = 0.33297581377 rad
Angle ∠ B = β = 51.00107406628° = 51°3″ = 0.89901308455 rad
Angle ∠ C = γ = 110.1065509788° = 110°6'20″ = 1.92217036704 rad

Height: ha = 22.5377468802
Height: hb = 9.39106120008
Height: hc = 7.77215409662

Median: ma = 26.14438329248
Median: mb = 18.06993109996
Median: mc = 11.30326545555

Inradius: r = 3.57773760003
Circumradius: R = 15.44109531548

Vertex coordinates: A[29; 0] B[0; 0] C[6.29331034483; 7.77215409662]
Centroid: CG[11.76443678161; 2.59105136554]
Coordinates of the circumscribed circle: U[14.5; -5.3087827647]
Coordinates of the inscribed circle: I[7.5; 3.57773760003]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.1066250451° = 161°6'22″ = 0.33297581377 rad
∠ B' = β' = 128.9999259337° = 128°59'57″ = 0.89901308455 rad
∠ C' = γ' = 69.89444902121° = 69°53'40″ = 1.92217036704 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 = 10 ; ; b = 24 ; ; c = 29 ; ;

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

p = a+b+c = 10+24+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 * (31.5-10)(31.5-24)(31.5-29) } ; ; T = sqrt{ 12698.44 } = 112.69 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 112.69 }{ 10 } = 22.54 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 112.69 }{ 24 } = 9.39 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 112.69 }{ 29 } = 7.77 ; ;

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{ 10**2-24**2-29**2 }{ 2 * 24 * 29 } ) = 18° 53'37" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-10**2-29**2 }{ 2 * 10 * 29 } ) = 51° 3" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-10**2-24**2 }{ 2 * 24 * 10 } ) = 110° 6'20" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 112.69 }{ 31.5 } = 3.58 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 18° 53'37" } = 15.44 ; ;




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