11 13 17 triangle

Acute scalene triangle.

Sides: a = 11   b = 13   c = 17

Area: T = 71.54995629357
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 40.32199178356° = 40°19'12″ = 0.70437153204 rad
Angle ∠ B = β = 49.8880417466° = 49°52'50″ = 0.87105775171 rad
Angle ∠ C = γ = 89.87996646984° = 89°47'59″ = 1.56772998162 rad

Height: ha = 132.9999205338
Height: hb = 110.9999327593
Height: hc = 8.41217132866

Median: ma = 14.09878721799
Median: mb = 12.75773508222
Median: mc = 8.52993610546

Inradius: r = 3.48877835578
Circumradius: R = 8.5500051959

Vertex coordinates: A[17; 0] B[0; 0] C[7.08882352941; 8.41217132866]
Centroid: CG[8.02994117647; 2.80439044289]
Coordinates of the circumscribed circle: U[8.5; 0.03297204614]
Coordinates of the inscribed circle: I[7.5; 3.48877835578]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.6880082164° = 139°40'48″ = 0.70437153204 rad
∠ B' = β' = 130.1219582534° = 130°7'10″ = 0.87105775171 rad
∠ C' = γ' = 90.22003353016° = 90°12'1″ = 1.56772998162 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 = 13 ; ; c = 17 ; ;

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

p = a+b+c = 11+13+17 = 41 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 41 }{ 2 } = 20.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.5 * (20.5-11)(20.5-13)(20.5-17) } ; ; T = sqrt{ 5112.19 } = 71.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 71.5 }{ 11 } = 13 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 71.5 }{ 13 } = 11 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 71.5 }{ 17 } = 8.41 ; ;

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**2-13**2-17**2 }{ 2 * 13 * 17 } ) = 40° 19'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-11**2-17**2 }{ 2 * 11 * 17 } ) = 49° 52'50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-11**2-13**2 }{ 2 * 13 * 11 } ) = 89° 47'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 71.5 }{ 20.5 } = 3.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 40° 19'12" } = 8.5 ; ;




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