9 12 17 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 12   c = 17

Area: T = 51.57551878329
Perimeter: p = 38
Semiperimeter: s = 19

Angle ∠ A = α = 30.37437861998° = 30°22'26″ = 0.53301225755 rad
Angle ∠ B = β = 42.39109285431° = 42°23'27″ = 0.74398612761 rad
Angle ∠ C = γ = 107.2355285257° = 107°14'7″ = 1.87216088021 rad

Height: ha = 11.46111528518
Height: hb = 8.59658646388
Height: hc = 6.06876691568

Median: ma = 14.00989257261
Median: mb = 12.20765556157
Median: mc = 6.34442887702

Inradius: r = 2.71444835702
Circumradius: R = 8.98996282764

Vertex coordinates: A[17; 0] B[0; 0] C[6.64770588235; 6.06876691568]
Centroid: CG[7.88223529412; 2.02325563856]
Coordinates of the circumscribed circle: U[8.5; -2.63769268967]
Coordinates of the inscribed circle: I[7; 2.71444835702]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.62662138° = 149°37'34″ = 0.53301225755 rad
∠ B' = β' = 137.6099071457° = 137°36'33″ = 0.74398612761 rad
∠ C' = γ' = 72.76547147429° = 72°45'53″ = 1.87216088021 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 = 12 ; ; c = 17 ; ;

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

p = a+b+c = 9+12+17 = 38 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 38 }{ 2 } = 19 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19 * (19-9)(19-12)(19-17) } ; ; T = sqrt{ 2660 } = 51.58 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 51.58 }{ 9 } = 11.46 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 51.58 }{ 12 } = 8.6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 51.58 }{ 17 } = 6.07 ; ;

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**2-12**2-17**2 }{ 2 * 12 * 17 } ) = 30° 22'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-9**2-17**2 }{ 2 * 9 * 17 } ) = 42° 23'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-9**2-12**2 }{ 2 * 12 * 9 } ) = 107° 14'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 51.58 }{ 19 } = 2.71 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 30° 22'26" } = 8.9 ; ;




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