4 16 17 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 16   c = 17

Area: T = 31.71765177786
Perimeter: p = 37
Semiperimeter: s = 18.5

Angle ∠ A = α = 13.48661135663° = 13°29'10″ = 0.2355377085 rad
Angle ∠ B = β = 68.88217401101° = 68°52'54″ = 1.20222131594 rad
Angle ∠ C = γ = 97.63221463237° = 97°37'56″ = 1.70440024091 rad

Height: ha = 15.85882588893
Height: hb = 3.96545647223
Height: hc = 3.73113550328

Median: ma = 16.38659696082
Median: mb = 9.40774438611
Median: mc = 7.98443597113

Inradius: r = 1.71444063664
Circumradius: R = 8.57659729961

Vertex coordinates: A[17; 0] B[0; 0] C[1.44111764706; 3.73113550328]
Centroid: CG[6.14770588235; 1.24437850109]
Coordinates of the circumscribed circle: U[8.5; -1.13989964135]
Coordinates of the inscribed circle: I[2.5; 1.71444063664]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.5143886434° = 166°30'50″ = 0.2355377085 rad
∠ B' = β' = 111.118825989° = 111°7'6″ = 1.20222131594 rad
∠ C' = γ' = 82.36878536763° = 82°22'4″ = 1.70440024091 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 = 16 ; ; c = 17 ; ;

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

p = a+b+c = 4+16+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 * (18.5-4)(18.5-16)(18.5-17) } ; ; T = sqrt{ 1005.94 } = 31.72 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 31.72 }{ 4 } = 15.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 31.72 }{ 16 } = 3.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 31.72 }{ 17 } = 3.73 ; ;

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**2-16**2-17**2 }{ 2 * 16 * 17 } ) = 13° 29'10" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-4**2-17**2 }{ 2 * 4 * 17 } ) = 68° 52'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-4**2-16**2 }{ 2 * 16 * 4 } ) = 97° 37'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 31.72 }{ 18.5 } = 1.71 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 13° 29'10" } = 8.58 ; ;




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