4 26 29 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 26   c = 29

Area: T = 36.28327438323
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 5.52327339087° = 5°31'22″ = 0.09663898904 rad
Angle ∠ B = β = 38.72436358425° = 38°43'25″ = 0.67658549438 rad
Angle ∠ C = γ = 135.7543630249° = 135°45'13″ = 2.36993478194 rad

Height: ha = 18.14113719161
Height: hb = 2.79109802948
Height: hc = 2.50222581953

Median: ma = 27.46881633896
Median: mb = 16.10990036936
Median: mc = 11.65111801977

Inradius: r = 1.23299235197
Circumradius: R = 20.78112287705

Vertex coordinates: A[29; 0] B[0; 0] C[3.12106896552; 2.50222581953]
Centroid: CG[10.70768965517; 0.83440860651]
Coordinates of the circumscribed circle: U[14.5; -14.88765533019]
Coordinates of the inscribed circle: I[3.5; 1.23299235197]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 174.4777266091° = 174°28'38″ = 0.09663898904 rad
∠ B' = β' = 141.2766364157° = 141°16'35″ = 0.67658549438 rad
∠ C' = γ' = 44.24663697513° = 44°14'47″ = 2.36993478194 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 = 4 ; ; b = 26 ; ; c = 29 ; ;

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

p = a+b+c = 4+26+29 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-4)(29.5-26)(29.5-29) } ; ; T = sqrt{ 1316.44 } = 36.28 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 36.28 }{ 4 } = 18.14 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 36.28 }{ 26 } = 2.79 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 36.28 }{ 29 } = 2.5 ; ;

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{ 4**2-26**2-29**2 }{ 2 * 26 * 29 } ) = 5° 31'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-4**2-29**2 }{ 2 * 4 * 29 } ) = 38° 43'25" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-4**2-26**2 }{ 2 * 26 * 4 } ) = 135° 45'13" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 36.28 }{ 29.5 } = 1.23 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 5° 31'22" } = 20.78 ; ;




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