4 8 9 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 8   c = 9

Area: T = 15.99880467558
Perimeter: p = 21
Semiperimeter: s = 10.5

Angle ∠ A = α = 26.38443297494° = 26°23'4″ = 0.46604934251 rad
Angle ∠ B = β = 62.7220387264° = 62°43'13″ = 1.09546772659 rad
Angle ∠ C = γ = 90.89552829866° = 90°53'43″ = 1.58664219626 rad

Height: ha = 7.99990233779
Height: hb = 43.9995116889
Height: hc = 3.55551215013

Median: ma = 8.27664726786
Median: mb = 5.70108771255
Median: mc = 4.44440972087

Inradius: r = 1.52436235006
Circumradius: R = 4.5010549417

Vertex coordinates: A[9; 0] B[0; 0] C[1.83333333333; 3.55551215013]
Centroid: CG[3.61111111111; 1.18550405004]
Coordinates of the circumscribed circle: U[4.5; -0.07703210846]
Coordinates of the inscribed circle: I[2.5; 1.52436235006]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.6165670251° = 153°36'56″ = 0.46604934251 rad
∠ B' = β' = 117.2879612736° = 117°16'47″ = 1.09546772659 rad
∠ C' = γ' = 89.10547170134° = 89°6'17″ = 1.58664219626 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 = 8 ; ; c = 9 ; ;

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

p = a+b+c = 4+8+9 = 21 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 21 }{ 2 } = 10.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 10.5 * (10.5-4)(10.5-8)(10.5-9) } ; ; T = sqrt{ 255.94 } = 16 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 16 }{ 4 } = 8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 16 }{ 8 } = 4 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 16 }{ 9 } = 3.56 ; ;

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**2-8**2-9**2 }{ 2 * 8 * 9 } ) = 26° 23'4" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 8**2-4**2-9**2 }{ 2 * 4 * 9 } ) = 62° 43'13" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 9**2-4**2-8**2 }{ 2 * 8 * 4 } ) = 90° 53'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 16 }{ 10.5 } = 1.52 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 26° 23'4" } = 4.5 ; ;




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