14 17 28 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 17   c = 28

Area: T = 92.59328587959
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 22.89551284418° = 22°53'42″ = 0.4399595374 rad
Angle ∠ B = β = 28.19110143445° = 28°11'28″ = 0.49220260198 rad
Angle ∠ C = γ = 128.9143857214° = 128°54'50″ = 2.25499712598 rad

Height: ha = 13.22875512566
Height: hb = 10.89332775054
Height: hc = 6.61437756283

Median: ma = 22.07994021658
Median: mb = 20.4398933436
Median: mc = 6.81990908485

Inradius: r = 3.13987409761
Circumradius: R = 17.99327482709

Vertex coordinates: A[28; 0] B[0; 0] C[12.33992857143; 6.61437756283]
Centroid: CG[13.44664285714; 2.20545918761]
Coordinates of the circumscribed circle: U[14; -11.30221675063]
Coordinates of the inscribed circle: I[12.5; 3.13987409761]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.1054871558° = 157°6'18″ = 0.4399595374 rad
∠ B' = β' = 151.8098985656° = 151°48'32″ = 0.49220260198 rad
∠ C' = γ' = 51.08661427862° = 51°5'10″ = 2.25499712598 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 = 17 ; ; c = 28 ; ;

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

p = a+b+c = 14+17+28 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-14)(29.5-17)(29.5-28) } ; ; T = sqrt{ 8573.44 } = 92.59 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 92.59 }{ 14 } = 13.23 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 92.59 }{ 17 } = 10.89 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 92.59 }{ 28 } = 6.61 ; ;

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**2-17**2-28**2 }{ 2 * 17 * 28 } ) = 22° 53'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-14**2-28**2 }{ 2 * 14 * 28 } ) = 28° 11'28" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-14**2-17**2 }{ 2 * 17 * 14 } ) = 128° 54'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 92.59 }{ 29.5 } = 3.14 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 22° 53'42" } = 17.99 ; ;




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