4 14 16 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 14   c = 16

Area: T = 25.74987863792
Perimeter: p = 34
Semiperimeter: s = 17

Angle ∠ A = α = 13.2911177243° = 13°17'28″ = 0.23219748044 rad
Angle ∠ B = β = 53.57664263577° = 53°34'35″ = 0.93550850414 rad
Angle ∠ C = γ = 113.1322396399° = 113°7'57″ = 1.97545328078 rad

Height: ha = 12.87443931896
Height: hb = 3.67883980542
Height: hc = 3.21985982974

Median: ma = 14.98996644258
Median: mb = 9.32773790531
Median: mc = 6.48107406984

Inradius: r = 1.51546344929
Circumradius: R = 8.69994391387

Vertex coordinates: A[16; 0] B[0; 0] C[2.375; 3.21985982974]
Centroid: CG[6.125; 1.07328660991]
Coordinates of the circumscribed circle: U[8; -3.41876368045]
Coordinates of the inscribed circle: I[3; 1.51546344929]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.7098822757° = 166°42'32″ = 0.23219748044 rad
∠ B' = β' = 126.4243573642° = 126°25'25″ = 0.93550850414 rad
∠ C' = γ' = 66.86876036007° = 66°52'3″ = 1.97545328078 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 = 14 ; ; c = 16 ; ;

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

p = a+b+c = 4+14+16 = 34 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 34 }{ 2 } = 17 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17 * (17-4)(17-14)(17-16) } ; ; T = sqrt{ 663 } = 25.75 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 25.75 }{ 4 } = 12.87 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 25.75 }{ 14 } = 3.68 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 25.75 }{ 16 } = 3.22 ; ;

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**2-14**2-16**2 }{ 2 * 14 * 16 } ) = 13° 17'28" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-4**2-16**2 }{ 2 * 4 * 16 } ) = 53° 34'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-4**2-14**2 }{ 2 * 14 * 4 } ) = 113° 7'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 25.75 }{ 17 } = 1.51 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 13° 17'28" } = 8.7 ; ;




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