8 12 17 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 12   c = 17

Area: T = 43.51993922292
Perimeter: p = 37
Semiperimeter: s = 18.5

Angle ∠ A = α = 25.25658261791° = 25°15'21″ = 0.44107973221 rad
Angle ∠ B = β = 39.79111530332° = 39°47'28″ = 0.69444866336 rad
Angle ∠ C = γ = 114.9533020788° = 114°57'11″ = 2.00663086979 rad

Height: ha = 10.88798480573
Height: hb = 7.25332320382
Height: hc = 5.12199284976

Median: ma = 14.16598022585
Median: mb = 11.85332695911
Median: mc = 5.63547138348

Inradius: r = 2.352239958
Circumradius: R = 9.37551309267

Vertex coordinates: A[17; 0] B[0; 0] C[6.14770588235; 5.12199284976]
Centroid: CG[7.71656862745; 1.70766428325]
Coordinates of the circumscribed circle: U[8.5; -3.95551333597]
Coordinates of the inscribed circle: I[6.5; 2.352239958]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.7444173821° = 154°44'39″ = 0.44107973221 rad
∠ B' = β' = 140.2098846967° = 140°12'32″ = 0.69444866336 rad
∠ C' = γ' = 65.04769792123° = 65°2'49″ = 2.00663086979 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 = 12 ; ; c = 17 ; ;

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

p = a+b+c = 8+12+17 = 37 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 37 }{ 2 } = 18.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18.5 * (18.5-8)(18.5-12)(18.5-17) } ; ; T = sqrt{ 1893.94 } = 43.52 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 43.52 }{ 8 } = 10.88 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 43.52 }{ 12 } = 7.25 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 43.52 }{ 17 } = 5.12 ; ;

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**2-12**2-17**2 }{ 2 * 12 * 17 } ) = 25° 15'21" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-8**2-17**2 }{ 2 * 8 * 17 } ) = 39° 47'28" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-8**2-12**2 }{ 2 * 12 * 8 } ) = 114° 57'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 43.52 }{ 18.5 } = 2.35 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 25° 15'21" } = 9.38 ; ;




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