7 24 29 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 24   c = 29

Area: T = 64.34328317686
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 10.65549054838° = 10°39'18″ = 0.18659631822 rad
Angle ∠ B = β = 39.34398936314° = 39°20'24″ = 0.68766106713 rad
Angle ∠ C = γ = 130.0055200885° = 130°19″ = 2.26990188002 rad

Height: ha = 18.38436662196
Height: hb = 5.36219026474
Height: hc = 4.43774366737

Median: ma = 26.38765496039
Median: mb = 17.34993515729
Median: mc = 10.11218742081

Inradius: r = 2.1454761059
Circumradius: R = 18.93298476073

Vertex coordinates: A[29; 0] B[0; 0] C[5.41437931034; 4.43774366737]
Centroid: CG[11.47112643678; 1.47991455579]
Coordinates of the circumscribed circle: U[14.5; -12.16991877475]
Coordinates of the inscribed circle: I[6; 2.1454761059]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.3455094516° = 169°20'42″ = 0.18659631822 rad
∠ B' = β' = 140.6660106369° = 140°39'36″ = 0.68766106713 rad
∠ C' = γ' = 49.99547991151° = 49°59'41″ = 2.26990188002 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 = 7 ; ; b = 24 ; ; c = 29 ; ;

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

p = a+b+c = 7+24+29 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-7)(30-24)(30-29) } ; ; T = sqrt{ 4140 } = 64.34 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 64.34 }{ 7 } = 18.38 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 64.34 }{ 24 } = 5.36 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 64.34 }{ 29 } = 4.44 ; ;

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{ 7**2-24**2-29**2 }{ 2 * 24 * 29 } ) = 10° 39'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-7**2-29**2 }{ 2 * 7 * 29 } ) = 39° 20'24" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-7**2-24**2 }{ 2 * 24 * 7 } ) = 130° 19" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 64.34 }{ 30 } = 2.14 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 10° 39'18" } = 18.93 ; ;




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