3 24 26 triangle

Obtuse scalene triangle.

Sides: a = 3   b = 24   c = 26

Area: T = 27.99004928272
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 5.13105088746° = 5°7'50″ = 0.09895442722 rad
Angle ∠ B = β = 45.67657648661° = 45°40'33″ = 0.79771924853 rad
Angle ∠ C = γ = 129.1943726259° = 129°11'37″ = 2.25548558961 rad

Height: ha = 18.66003285515
Height: hb = 2.32550410689
Height: hc = 2.14661917559

Median: ma = 24.97549874875
Median: mb = 14.08990028036
Median: mc = 11.11330553854

Inradius: r = 1.05328487859
Circumradius: R = 16.77438972533

Vertex coordinates: A[26; 0] B[0; 0] C[2.09661538462; 2.14661917559]
Centroid: CG[9.36553846154; 0.7155397252]
Coordinates of the circumscribed circle: U[13; -10.66001711809]
Coordinates of the inscribed circle: I[2.5; 1.05328487859]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 174.8699491125° = 174°52'10″ = 0.09895442722 rad
∠ B' = β' = 134.3244235134° = 134°19'27″ = 0.79771924853 rad
∠ C' = γ' = 50.80662737407° = 50°48'23″ = 2.25548558961 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 = 3 ; ; b = 24 ; ; c = 26 ; ;

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

p = a+b+c = 3+24+26 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-3)(26.5-24)(26.5-26) } ; ; T = sqrt{ 778.44 } = 27.9 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 27.9 }{ 3 } = 18.6 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 27.9 }{ 24 } = 2.33 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 27.9 }{ 26 } = 2.15 ; ;

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{ 3**2-24**2-26**2 }{ 2 * 24 * 26 } ) = 5° 7'50" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-3**2-26**2 }{ 2 * 3 * 26 } ) = 45° 40'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-3**2-24**2 }{ 2 * 24 * 3 } ) = 129° 11'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 27.9 }{ 26.5 } = 1.05 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 5° 7'50" } = 16.77 ; ;




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