11 14 17 triangle

Acute scalene triangle.

Sides: a = 11   b = 14   c = 17

Area: T = 76.68111580507
Perimeter: p = 42
Semiperimeter: s = 21

Angle ∠ A = α = 40.11991668984° = 40°7'9″ = 0.77002115555 rad
Angle ∠ B = β = 55.0976741672° = 55°5'48″ = 0.96216195493 rad
Angle ∠ C = γ = 84.78440914295° = 84°47'3″ = 1.48797615488 rad

Height: ha = 13.94220287365
Height: hb = 10.95444511501
Height: hc = 9.02113127118

Median: ma = 14.56988022843
Median: mb = 12.49899959968
Median: mc = 9.28770878105

Inradius: r = 3.65114837167
Circumradius: R = 8.53553431878

Vertex coordinates: A[17; 0] B[0; 0] C[6.29441176471; 9.02113127118]
Centroid: CG[7.76547058824; 3.00771042373]
Coordinates of the circumscribed circle: U[8.5; 0.77659402898]
Coordinates of the inscribed circle: I[7; 3.65114837167]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.8810833102° = 139°52'51″ = 0.77002115555 rad
∠ B' = β' = 124.9033258328° = 124°54'12″ = 0.96216195493 rad
∠ C' = γ' = 95.21659085705° = 95°12'57″ = 1.48797615488 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 = 11 ; ; b = 14 ; ; c = 17 ; ;

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

p = a+b+c = 11+14+17 = 42 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 42 }{ 2 } = 21 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21 * (21-11)(21-14)(21-17) } ; ; T = sqrt{ 5880 } = 76.68 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 76.68 }{ 11 } = 13.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 76.68 }{ 14 } = 10.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 76.68 }{ 17 } = 9.02 ; ;

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{ 11**2-14**2-17**2 }{ 2 * 14 * 17 } ) = 40° 7'9" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-11**2-17**2 }{ 2 * 11 * 17 } ) = 55° 5'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-11**2-14**2 }{ 2 * 14 * 11 } ) = 84° 47'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 76.68 }{ 21 } = 3.65 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 40° 7'9" } = 8.54 ; ;




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