24 26 29 triangle

Acute scalene triangle.

Sides: a = 24   b = 26   c = 29

Area: T = 294.5955379292
Perimeter: p = 79
Semiperimeter: s = 39.5

Angle ∠ A = α = 51.39107833262° = 51°23'27″ = 0.89769383742 rad
Angle ∠ B = β = 57.83771442373° = 57°50'14″ = 1.00994485969 rad
Angle ∠ C = γ = 70.77220724365° = 70°46'19″ = 1.23552056825 rad

Height: ha = 24.5549614941
Height: hb = 22.66111830224
Height: hc = 20.31769227098

Median: ma = 24.78991105125
Median: mb = 23.22771392987
Median: mc = 20.39899485041

Inradius: r = 7.45881108681
Circumradius: R = 15.35766563429

Vertex coordinates: A[29; 0] B[0; 0] C[12.7765862069; 20.31769227098]
Centroid: CG[13.92552873563; 6.77223075699]
Coordinates of the circumscribed circle: U[14.5; 5.05773603822]
Coordinates of the inscribed circle: I[13.5; 7.45881108681]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.6099216674° = 128°36'33″ = 0.89769383742 rad
∠ B' = β' = 122.1632855763° = 122°9'46″ = 1.00994485969 rad
∠ C' = γ' = 109.2287927563° = 109°13'41″ = 1.23552056825 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 = 24 ; ; b = 26 ; ; c = 29 ; ;

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

p = a+b+c = 24+26+29 = 79 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 79 }{ 2 } = 39.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 39.5 * (39.5-24)(39.5-26)(39.5-29) } ; ; T = sqrt{ 86786.44 } = 294.6 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 294.6 }{ 24 } = 24.55 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 294.6 }{ 26 } = 22.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 294.6 }{ 29 } = 20.32 ; ;

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{ 24**2-26**2-29**2 }{ 2 * 26 * 29 } ) = 51° 23'27" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-24**2-29**2 }{ 2 * 24 * 29 } ) = 57° 50'14" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-24**2-26**2 }{ 2 * 26 * 24 } ) = 70° 46'19" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 294.6 }{ 39.5 } = 7.46 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 24 }{ 2 * sin 51° 23'27" } = 15.36 ; ;




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