9 14 16 triangle

Acute scalene triangle.

Sides: a = 9   b = 14   c = 16

Area: T = 62.78108689013
Perimeter: p = 39
Semiperimeter: s = 19.5

Angle ∠ A = α = 34.09333908114° = 34°5'36″ = 0.59550419228 rad
Angle ∠ B = β = 60.68768010358° = 60°41'12″ = 1.05991844906 rad
Angle ∠ C = γ = 85.22198081528° = 85°13'11″ = 1.48773662402 rad

Height: ha = 13.95113042003
Height: hb = 8.96986955573
Height: hc = 7.84876086127

Median: ma = 14.34439882878
Median: mb = 10.93216055545
Median: mc = 8.63113382508

Inradius: r = 3.22195317385
Circumradius: R = 8.02879232961

Vertex coordinates: A[16; 0] B[0; 0] C[4.406625; 7.84876086127]
Centroid: CG[6.80220833333; 2.61658695376]
Coordinates of the circumscribed circle: U[8; 0.6698993608]
Coordinates of the inscribed circle: I[5.5; 3.22195317385]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.9076609189° = 145°54'24″ = 0.59550419228 rad
∠ B' = β' = 119.3133198964° = 119°18'48″ = 1.05991844906 rad
∠ C' = γ' = 94.78801918472° = 94°46'49″ = 1.48773662402 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 = 14 ; ; c = 16 ; ;

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

p = a+b+c = 9+14+16 = 39 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 39 }{ 2 } = 19.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19.5 * (19.5-9)(19.5-14)(19.5-16) } ; ; T = sqrt{ 3941.44 } = 62.78 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 62.78 }{ 9 } = 13.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 62.78 }{ 14 } = 8.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 62.78 }{ 16 } = 7.85 ; ;

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**2-14**2-16**2 }{ 2 * 14 * 16 } ) = 34° 5'36" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-9**2-16**2 }{ 2 * 9 * 16 } ) = 60° 41'12" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-9**2-14**2 }{ 2 * 14 * 9 } ) = 85° 13'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 62.78 }{ 19.5 } = 3.22 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 34° 5'36" } = 8.03 ; ;




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