3 17 19 triangle

Obtuse scalene triangle.

Sides: a = 3   b = 17   c = 19

Area: T = 20.05546129357
Perimeter: p = 39
Semiperimeter: s = 19.5

Angle ∠ A = α = 7.1333240874° = 7°8' = 0.12444985396 rad
Angle ∠ B = β = 44.72222460248° = 44°43'20″ = 0.7810550442 rad
Angle ∠ C = γ = 128.1454513101° = 128°8'40″ = 2.2376543672 rad

Height: ha = 13.37697419571
Height: hb = 2.35993662277
Height: hc = 2.1111011888

Median: ma = 17.96552442232
Median: mb = 10.61883802908
Median: mc = 7.66548548584

Inradius: r = 1.0288441689
Circumradius: R = 12.08795151109

Vertex coordinates: A[19; 0] B[0; 0] C[2.13215789474; 2.1111011888]
Centroid: CG[7.04438596491; 0.70436706293]
Coordinates of the circumscribed circle: U[9.5; -7.46108769803]
Coordinates of the inscribed circle: I[2.5; 1.0288441689]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 172.8676759126° = 172°52' = 0.12444985396 rad
∠ B' = β' = 135.2787753975° = 135°16'40″ = 0.7810550442 rad
∠ C' = γ' = 51.85554868988° = 51°51'20″ = 2.2376543672 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 = 3 ; ; b = 17 ; ; c = 19 ; ;

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

p = a+b+c = 3+17+19 = 39 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 39 }{ 2 } = 19.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19.5 * (19.5-3)(19.5-17)(19.5-19) } ; ; T = sqrt{ 402.19 } = 20.05 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 20.05 }{ 3 } = 13.37 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 20.05 }{ 17 } = 2.36 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 20.05 }{ 19 } = 2.11 ; ;

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{ 3**2-17**2-19**2 }{ 2 * 17 * 19 } ) = 7° 8' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-3**2-19**2 }{ 2 * 3 * 19 } ) = 44° 43'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-3**2-17**2 }{ 2 * 17 * 3 } ) = 128° 8'40" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 20.05 }{ 19.5 } = 1.03 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 7° 8' } = 12.08 ; ;




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