7 26 29 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 26   c = 29

Area: T = 86.25554346114
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 13.22660949708° = 13°13'34″ = 0.23108389044 rad
Angle ∠ B = β = 58.19107096653° = 58°11'27″ = 1.01656194777 rad
Angle ∠ C = γ = 108.5833195364° = 108°35' = 1.89551342714 rad

Height: ha = 24.6444409889
Height: hb = 6.63550334316
Height: hc = 5.94986506629

Median: ma = 27.31875767593
Median: mb = 16.61332477258
Median: mc = 12.33989626793

Inradius: r = 2.78224333746
Circumradius: R = 15.29875868239

Vertex coordinates: A[29; 0] B[0; 0] C[3.69896551724; 5.94986506629]
Centroid: CG[10.89765517241; 1.98328835543]
Coordinates of the circumscribed circle: U[14.5; -4.87550551417]
Coordinates of the inscribed circle: I[5; 2.78224333746]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.7743905029° = 166°46'26″ = 0.23108389044 rad
∠ B' = β' = 121.8099290335° = 121°48'33″ = 1.01656194777 rad
∠ C' = γ' = 71.41768046361° = 71°25' = 1.89551342714 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 = 26 ; ; c = 29 ; ;

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

p = a+b+c = 7+26+29 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-7)(31-26)(31-29) } ; ; T = sqrt{ 7440 } = 86.26 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 86.26 }{ 7 } = 24.64 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 86.26 }{ 26 } = 6.64 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 86.26 }{ 29 } = 5.95 ; ;

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**2-26**2-29**2 }{ 2 * 26 * 29 } ) = 13° 13'34" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-7**2-29**2 }{ 2 * 7 * 29 } ) = 58° 11'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-7**2-26**2 }{ 2 * 26 * 7 } ) = 108° 35' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 86.26 }{ 31 } = 2.78 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 13° 13'34" } = 15.3 ; ;




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