9 29 30 triangle

Acute scalene triangle.

Sides: a = 9   b = 29   c = 30

Area: T = 130.3844048104
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 17.44215938563° = 17°26'30″ = 0.30444132396 rad
Angle ∠ B = β = 74.97438862409° = 74°58'26″ = 1.30985411679 rad
Angle ∠ C = γ = 87.58545199028° = 87°35'4″ = 1.52986382461 rad

Height: ha = 28.9744232912
Height: hb = 8.99220033175
Height: hc = 8.69222698736

Median: ma = 29.15990466236
Median: mb = 16.74106690428
Median: mc = 15.36222914957

Inradius: r = 3.83548249442
Circumradius: R = 15.01333396567

Vertex coordinates: A[30; 0] B[0; 0] C[2.33333333333; 8.69222698736]
Centroid: CG[10.77877777778; 2.89774232912]
Coordinates of the circumscribed circle: U[15; 0.63327461158]
Coordinates of the inscribed circle: I[5; 3.83548249442]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.5588406144° = 162°33'30″ = 0.30444132396 rad
∠ B' = β' = 105.0266113759° = 105°1'34″ = 1.30985411679 rad
∠ C' = γ' = 92.41554800972° = 92°24'56″ = 1.52986382461 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 = 9 ; ; b = 29 ; ; c = 30 ; ;

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

p = a+b+c = 9+29+30 = 68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 68 }{ 2 } = 34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34 * (34-9)(34-29)(34-30) } ; ; T = sqrt{ 17000 } = 130.38 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 130.38 }{ 9 } = 28.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 130.38 }{ 29 } = 8.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 130.38 }{ 30 } = 8.69 ; ;

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{ 9**2-29**2-30**2 }{ 2 * 29 * 30 } ) = 17° 26'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-9**2-30**2 }{ 2 * 9 * 30 } ) = 74° 58'26" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-9**2-29**2 }{ 2 * 29 * 9 } ) = 87° 35'4" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 130.38 }{ 34 } = 3.83 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 17° 26'30" } = 15.01 ; ;




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