11 17 19 triangle

Acute scalene triangle.

Sides: a = 11   b = 17   c = 19

Area: T = 92.69440532073
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 35.02766219513° = 35°1'36″ = 0.61113298789 rad
Angle ∠ B = β = 62.5021687524° = 62°30'6″ = 1.09108602353 rad
Angle ∠ C = γ = 82.47216905248° = 82°28'18″ = 1.43994025393 rad

Height: ha = 16.85334642195
Height: hb = 10.90551827303
Height: hc = 9.75772687587

Median: ma = 17.16882847134
Median: mb = 12.99903810568
Median: mc = 10.71221426428

Inradius: r = 3.94444277961
Circumradius: R = 9.58325996303

Vertex coordinates: A[19; 0] B[0; 0] C[5.07989473684; 9.75772687587]
Centroid: CG[8.02663157895; 3.25224229196]
Coordinates of the circumscribed circle: U[9.5; 1.25554742831]
Coordinates of the inscribed circle: I[6.5; 3.94444277961]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.9733378049° = 144°58'24″ = 0.61113298789 rad
∠ B' = β' = 117.4988312476° = 117°29'54″ = 1.09108602353 rad
∠ C' = γ' = 97.52883094752° = 97°31'42″ = 1.43994025393 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 = 17 ; ; c = 19 ; ;

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

p = a+b+c = 11+17+19 = 47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 47 }{ 2 } = 23.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23.5 * (23.5-11)(23.5-17)(23.5-19) } ; ; T = sqrt{ 8592.19 } = 92.69 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 92.69 }{ 11 } = 16.85 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 92.69 }{ 17 } = 10.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 92.69 }{ 19 } = 9.76 ; ;

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**2-17**2-19**2 }{ 2 * 17 * 19 } ) = 35° 1'36" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-11**2-19**2 }{ 2 * 11 * 19 } ) = 62° 30'6" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-11**2-17**2 }{ 2 * 17 * 11 } ) = 82° 28'18" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 92.69 }{ 23.5 } = 3.94 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 35° 1'36" } = 9.58 ; ;




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