8 11 17 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 11   c = 17

Area: T = 35.49664786986
Perimeter: p = 36
Semiperimeter: s = 18

Angle ∠ A = α = 22.31114770869° = 22°18'41″ = 0.38994087361 rad
Angle ∠ B = β = 31.46769762933° = 31°28'1″ = 0.5499202342 rad
Angle ∠ C = γ = 126.222154662° = 126°13'18″ = 2.20329815755 rad

Height: ha = 8.87441196746
Height: hb = 6.45439052179
Height: hc = 4.17660563175

Median: ma = 13.74877270849
Median: mb = 12.09333866224
Median: mc = 4.5

Inradius: r = 1.97220265944
Circumradius: R = 10.53662563756

Vertex coordinates: A[17; 0] B[0; 0] C[6.82435294118; 4.17660563175]
Centroid: CG[7.94111764706; 1.39220187725]
Coordinates of the circumscribed circle: U[8.5; -6.22659696765]
Coordinates of the inscribed circle: I[7; 1.97220265944]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.6898522913° = 157°41'19″ = 0.38994087361 rad
∠ B' = β' = 148.5333023707° = 148°31'59″ = 0.5499202342 rad
∠ C' = γ' = 53.77884533802° = 53°46'42″ = 2.20329815755 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 = 8 ; ; b = 11 ; ; c = 17 ; ;

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

p = a+b+c = 8+11+17 = 36 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 36 }{ 2 } = 18 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18 * (18-8)(18-11)(18-17) } ; ; T = sqrt{ 1260 } = 35.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 35.5 }{ 8 } = 8.87 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 35.5 }{ 11 } = 6.45 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 35.5 }{ 17 } = 4.18 ; ;

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{ 8**2-11**2-17**2 }{ 2 * 11 * 17 } ) = 22° 18'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-8**2-17**2 }{ 2 * 8 * 17 } ) = 31° 28'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-8**2-11**2 }{ 2 * 11 * 8 } ) = 126° 13'18" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 35.5 }{ 18 } = 1.97 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 22° 18'41" } = 10.54 ; ;




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