8 29 30 triangle

Acute scalene triangle.

Sides: a = 8   b = 29   c = 30

Area: T = 115.9933264891
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 15.46550895141° = 15°27'54″ = 0.27699167311 rad
Angle ∠ B = β = 75.15223338526° = 75°9'8″ = 1.31216556663 rad
Angle ∠ C = γ = 89.38325766333° = 89°22'57″ = 1.56600202562 rad

Height: ha = 28.99883162227
Height: hb = 87.9995355097
Height: hc = 7.7332884326

Median: ma = 29.23218319645
Median: mb = 16.48548415218
Median: mc = 15.0833103129

Inradius: r = 3.46224855191
Circumradius: R = 15.00108709699

Vertex coordinates: A[30; 0] B[0; 0] C[2.05; 7.7332884326]
Centroid: CG[10.68333333333; 2.57876281087]
Coordinates of the circumscribed circle: U[15; 0.16216473165]
Coordinates of the inscribed circle: I[4.5; 3.46224855191]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.5354910486° = 164°32'6″ = 0.27699167311 rad
∠ B' = β' = 104.8487666147° = 104°50'52″ = 1.31216556663 rad
∠ C' = γ' = 90.61774233667° = 90°37'3″ = 1.56600202562 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 = 29 ; ; c = 30 ; ;

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

p = a+b+c = 8+29+30 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-8)(33.5-29)(33.5-30) } ; ; T = sqrt{ 13454.44 } = 115.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 115.99 }{ 8 } = 29 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 115.99 }{ 29 } = 8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 115.99 }{ 30 } = 7.73 ; ;

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**2-29**2-30**2 }{ 2 * 29 * 30 } ) = 15° 27'54" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-8**2-30**2 }{ 2 * 8 * 30 } ) = 75° 9'8" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-8**2-29**2 }{ 2 * 29 * 8 } ) = 89° 22'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 115.99 }{ 33.5 } = 3.46 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 15° 27'54" } = 15 ; ;




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