2 8 9 triangle

Obtuse scalene triangle.

Sides: a = 2   b = 8   c = 9

Area: T = 7.31100957586
Perimeter: p = 19
Semiperimeter: s = 9.5

Angle ∠ A = α = 11.71658523949° = 11°42'57″ = 0.2044480199 rad
Angle ∠ B = β = 54.31546652873° = 54°18'53″ = 0.94879697414 rad
Angle ∠ C = γ = 113.9699482318° = 113°58'10″ = 1.98991427132 rad

Height: ha = 7.31100957586
Height: hb = 1.82875239397
Height: hc = 1.62444657241

Median: ma = 8.45657672626
Median: mb = 5.14878150705
Median: mc = 3.70880992435

Inradius: r = 0.76994837641
Circumradius: R = 4.925469609

Vertex coordinates: A[9; 0] B[0; 0] C[1.16766666667; 1.62444657241]
Centroid: CG[3.38988888889; 0.54114885747]
Coordinates of the circumscribed circle: U[4.5; -2.00106577866]
Coordinates of the inscribed circle: I[1.5; 0.76994837641]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.2844147605° = 168°17'3″ = 0.2044480199 rad
∠ B' = β' = 125.6855334713° = 125°41'7″ = 0.94879697414 rad
∠ C' = γ' = 66.03105176822° = 66°1'50″ = 1.98991427132 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 = 2 ; ; b = 8 ; ; c = 9 ; ;

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

p = a+b+c = 2+8+9 = 19 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 19 }{ 2 } = 9.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 9.5 * (9.5-2)(9.5-8)(9.5-9) } ; ; T = sqrt{ 53.44 } = 7.31 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 7.31 }{ 2 } = 7.31 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 7.31 }{ 8 } = 1.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 7.31 }{ 9 } = 1.62 ; ;

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{ 2**2-8**2-9**2 }{ 2 * 8 * 9 } ) = 11° 42'57" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 8**2-2**2-9**2 }{ 2 * 2 * 9 } ) = 54° 18'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 9**2-2**2-8**2 }{ 2 * 8 * 2 } ) = 113° 58'10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 7.31 }{ 9.5 } = 0.77 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 11° 42'57" } = 4.92 ; ;




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