10 17 19 triangle

Acute scalene triangle.

Sides: a = 10   b = 17   c = 19

Area: T = 84.71112743382
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 31.63664748535° = 31°38'11″ = 0.55221606499 rad
Angle ∠ B = β = 63.08773509057° = 63°5'14″ = 1.10110819897 rad
Angle ∠ C = γ = 85.27661742408° = 85°16'34″ = 1.4888350014 rad

Height: ha = 16.94222548676
Height: hb = 9.96660322751
Height: hc = 8.91769762461

Median: ma = 17.32105080757
Median: mb = 12.58797456254
Median: mc = 10.21102889283

Inradius: r = 3.68330988843
Circumradius: R = 9.53223793239

Vertex coordinates: A[19; 0] B[0; 0] C[4.52663157895; 8.91769762461]
Centroid: CG[7.84221052632; 2.97223254154]
Coordinates of the circumscribed circle: U[9.5; 0.78550194737]
Coordinates of the inscribed circle: I[6; 3.68330988843]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.3643525146° = 148°21'49″ = 0.55221606499 rad
∠ B' = β' = 116.9132649094° = 116°54'46″ = 1.10110819897 rad
∠ C' = γ' = 94.72438257592° = 94°43'26″ = 1.4888350014 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 = 10 ; ; b = 17 ; ; c = 19 ; ;

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

p = a+b+c = 10+17+19 = 46 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 46 }{ 2 } = 23 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23 * (23-10)(23-17)(23-19) } ; ; T = sqrt{ 7176 } = 84.71 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 84.71 }{ 10 } = 16.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 84.71 }{ 17 } = 9.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 84.71 }{ 19 } = 8.92 ; ;

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{ 10**2-17**2-19**2 }{ 2 * 17 * 19 } ) = 31° 38'11" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-10**2-19**2 }{ 2 * 10 * 19 } ) = 63° 5'14" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-10**2-17**2 }{ 2 * 17 * 10 } ) = 85° 16'34" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 84.71 }{ 23 } = 3.68 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 31° 38'11" } = 9.53 ; ;




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