14 16 17 triangle

Acute scalene triangle.

Sides: a = 14   b = 16   c = 17

Area: T = 104.3243714945
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 50.09329429377° = 50°5'35″ = 0.87442867863 rad
Angle ∠ B = β = 61.24332248734° = 61°14'36″ = 1.06988959186 rad
Angle ∠ C = γ = 68.66438321889° = 68°39'50″ = 1.19884099487 rad

Height: ha = 14.90333878493
Height: hb = 13.04404643682
Height: hc = 12.27333782289

Median: ma = 14.95499163877
Median: mb = 13.36603892159
Median: mc = 12.43995967676

Inradius: r = 4.4399307019
Circumradius: R = 9.12554419045

Vertex coordinates: A[17; 0] B[0; 0] C[6.73552941176; 12.27333782289]
Centroid: CG[7.91217647059; 4.09111260763]
Coordinates of the circumscribed circle: U[8.5; 3.32201942644]
Coordinates of the inscribed circle: I[7.5; 4.4399307019]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 129.9077057062° = 129°54'25″ = 0.87442867863 rad
∠ B' = β' = 118.7576775127° = 118°45'24″ = 1.06988959186 rad
∠ C' = γ' = 111.3366167811° = 111°20'10″ = 1.19884099487 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 = 14 ; ; b = 16 ; ; c = 17 ; ;

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

p = a+b+c = 14+16+17 = 47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 47 }{ 2 } = 23.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23.5 * (23.5-14)(23.5-16)(23.5-17) } ; ; T = sqrt{ 10883.44 } = 104.32 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 104.32 }{ 14 } = 14.9 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 104.32 }{ 16 } = 13.04 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 104.32 }{ 17 } = 12.27 ; ;

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{ 14**2-16**2-17**2 }{ 2 * 16 * 17 } ) = 50° 5'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-14**2-17**2 }{ 2 * 14 * 17 } ) = 61° 14'36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-14**2-16**2 }{ 2 * 16 * 14 } ) = 68° 39'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 104.32 }{ 23.5 } = 4.44 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 50° 5'35" } = 9.13 ; ;




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