8 27 29 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 27   c = 29

Area: T = 107.331126292
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 15.91216001663° = 15°54'42″ = 0.27877098122 rad
Angle ∠ B = β = 67.70990296252° = 67°42'33″ = 1.18217455003 rad
Angle ∠ C = γ = 96.37993702084° = 96°22'46″ = 1.68221373411 rad

Height: ha = 26.833281573
Height: hb = 7.955046392
Height: hc = 7.40221560634

Median: ma = 27.73108492477
Median: mb = 16.43992822228
Median: mc = 13.6477344064

Inradius: r = 3.35441019662
Circumradius: R = 14.59903435532

Vertex coordinates: A[29; 0] B[0; 0] C[3.03444827586; 7.40221560634]
Centroid: CG[10.67881609195; 2.46773853545]
Coordinates of the circumscribed circle: U[14.5; -1.62111492837]
Coordinates of the inscribed circle: I[5; 3.35441019662]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.0888399834° = 164°5'18″ = 0.27877098122 rad
∠ B' = β' = 112.2910970375° = 112°17'27″ = 1.18217455003 rad
∠ C' = γ' = 83.62106297916° = 83°37'14″ = 1.68221373411 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 = 8 ; ; b = 27 ; ; c = 29 ; ;

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

p = a+b+c = 8+27+29 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-8)(32-27)(32-29) } ; ; T = sqrt{ 11520 } = 107.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 107.33 }{ 8 } = 26.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 107.33 }{ 27 } = 7.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 107.33 }{ 29 } = 7.4 ; ;

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{ 8**2-27**2-29**2 }{ 2 * 27 * 29 } ) = 15° 54'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-8**2-29**2 }{ 2 * 8 * 29 } ) = 67° 42'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-8**2-27**2 }{ 2 * 27 * 8 } ) = 96° 22'46" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 107.33 }{ 32 } = 3.35 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 15° 54'42" } = 14.59 ; ;




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