3 14 16 triangle

Obtuse scalene triangle.

Sides: a = 3   b = 14   c = 16

Area: T = 16.6866446596
Perimeter: p = 33
Semiperimeter: s = 16.5

Angle ∠ A = α = 8.56881759081° = 8°34'5″ = 0.15495428805 rad
Angle ∠ B = β = 44.04986256741° = 44°2'55″ = 0.7698793549 rad
Angle ∠ C = γ = 127.3833198418° = 127°23' = 2.22332562241 rad

Height: ha = 11.12442977306
Height: hb = 2.38437780851
Height: hc = 2.08658058245

Median: ma = 14.95882753017
Median: mb = 9.13878334412
Median: mc = 6.2054836823

Inradius: r = 1.01112997937
Circumradius: R = 10.06880512795

Vertex coordinates: A[16; 0] B[0; 0] C[2.156625; 2.08658058245]
Centroid: CG[6.05220833333; 0.69552686082]
Coordinates of the circumscribed circle: U[8; -6.11327454197]
Coordinates of the inscribed circle: I[2.5; 1.01112997937]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 171.4321824092° = 171°25'55″ = 0.15495428805 rad
∠ B' = β' = 135.9511374326° = 135°57'5″ = 0.7698793549 rad
∠ C' = γ' = 52.61768015821° = 52°37' = 2.22332562241 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 = 3 ; ; b = 14 ; ; c = 16 ; ;

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

p = a+b+c = 3+14+16 = 33 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 33 }{ 2 } = 16.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16.5 * (16.5-3)(16.5-14)(16.5-16) } ; ; T = sqrt{ 278.44 } = 16.69 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 16.69 }{ 3 } = 11.12 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 16.69 }{ 14 } = 2.38 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 16.69 }{ 16 } = 2.09 ; ;

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{ 3**2-14**2-16**2 }{ 2 * 14 * 16 } ) = 8° 34'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-3**2-16**2 }{ 2 * 3 * 16 } ) = 44° 2'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-3**2-14**2 }{ 2 * 14 * 3 } ) = 127° 23' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 16.69 }{ 16.5 } = 1.01 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 8° 34'5" } = 10.07 ; ;




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