5 14 17 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 14   c = 17

Area: T = 30.59441170816
Perimeter: p = 36
Semiperimeter: s = 18

Angle ∠ A = α = 14.89876656557° = 14°53'52″ = 0.26600133166 rad
Angle ∠ B = β = 46.04330532762° = 46°2'35″ = 0.80436028773 rad
Angle ∠ C = γ = 119.0599281068° = 119°3'33″ = 2.07879764597 rad

Height: ha = 12.23876468326
Height: hb = 4.37105881545
Height: hc = 3.59993078919

Median: ma = 15.37704261489
Median: mb = 10.39223048454
Median: mc = 6.18546584384

Inradius: r = 1.76996731712
Circumradius: R = 9.72440917006

Vertex coordinates: A[17; 0] B[0; 0] C[3.47105882353; 3.59993078919]
Centroid: CG[6.82435294118; 1.21997692973]
Coordinates of the circumscribed circle: U[8.5; -4.72331302546]
Coordinates of the inscribed circle: I[4; 1.76996731712]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.1022334344° = 165°6'8″ = 0.26600133166 rad
∠ B' = β' = 133.9576946724° = 133°57'25″ = 0.80436028773 rad
∠ C' = γ' = 60.9410718932° = 60°56'27″ = 2.07879764597 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 = 5 ; ; b = 14 ; ; c = 17 ; ;

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

p = a+b+c = 5+14+17 = 36 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 36 }{ 2 } = 18 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18 * (18-5)(18-14)(18-17) } ; ; T = sqrt{ 936 } = 30.59 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 30.59 }{ 5 } = 12.24 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 30.59 }{ 14 } = 4.37 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 30.59 }{ 17 } = 3.6 ; ;

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{ 5**2-14**2-17**2 }{ 2 * 14 * 17 } ) = 14° 53'52" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-5**2-17**2 }{ 2 * 5 * 17 } ) = 46° 2'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-5**2-14**2 }{ 2 * 14 * 5 } ) = 119° 3'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 30.59 }{ 18 } = 1.7 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 14° 53'52" } = 9.72 ; ;




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