17 23 27 triangle

Acute scalene triangle.

Sides: a = 17   b = 23   c = 27

Area: T = 194.2329728672
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 38.72217286208° = 38°43'18″ = 0.67658216565 rad
Angle ∠ B = β = 57.81333065911° = 57°48'48″ = 1.00990325515 rad
Angle ∠ C = γ = 83.46549647881° = 83°27'54″ = 1.45767384456 rad

Height: ha = 22.85105563144
Height: hb = 16.89895416237
Height: hc = 14.3877387309

Median: ma = 23.5965550428
Median: mb = 19.41100489438
Median: mc = 15.05882203464

Inradius: r = 5.79879023484
Circumradius: R = 13.58882906188

Vertex coordinates: A[27; 0] B[0; 0] C[9.05655555556; 14.3877387309]
Centroid: CG[12.01985185185; 4.79657957697]
Coordinates of the circumscribed circle: U[13.5; 1.54664934336]
Coordinates of the inscribed circle: I[10.5; 5.79879023484]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.2788271379° = 141°16'42″ = 0.67658216565 rad
∠ B' = β' = 122.1876693409° = 122°11'12″ = 1.00990325515 rad
∠ C' = γ' = 96.53550352119° = 96°32'6″ = 1.45767384456 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 = 17 ; ; b = 23 ; ; c = 27 ; ;

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

p = a+b+c = 17+23+27 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-17)(33.5-23)(33.5-27) } ; ; T = sqrt{ 37725.19 } = 194.23 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 194.23 }{ 17 } = 22.85 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 194.23 }{ 23 } = 16.89 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 194.23 }{ 27 } = 14.39 ; ;

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{ 17**2-23**2-27**2 }{ 2 * 23 * 27 } ) = 38° 43'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-17**2-27**2 }{ 2 * 17 * 27 } ) = 57° 48'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-17**2-23**2 }{ 2 * 23 * 17 } ) = 83° 27'54" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 194.23 }{ 33.5 } = 5.8 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 38° 43'18" } = 13.59 ; ;




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