4 19 19 triangle

Acute isosceles triangle.

Sides: a = 4   b = 19   c = 19

Area: T = 37.78988872554
Perimeter: p = 42
Semiperimeter: s = 21

Angle ∠ A = α = 12.08546568381° = 12°5'5″ = 0.21109170508 rad
Angle ∠ B = β = 83.95876715809° = 83°57'28″ = 1.46553378014 rad
Angle ∠ C = γ = 83.95876715809° = 83°57'28″ = 1.46553378014 rad

Height: ha = 18.89444436277
Height: hb = 3.97877776058
Height: hc = 3.97877776058

Median: ma = 18.89444436277
Median: mb = 9.91221138008
Median: mc = 9.91221138008

Inradius: r = 1.79994708217
Circumradius: R = 9.55330730387

Vertex coordinates: A[19; 0] B[0; 0] C[0.42110526316; 3.97877776058]
Centroid: CG[6.47436842105; 1.32659258686]
Coordinates of the circumscribed circle: U[9.5; 1.00655866356]
Coordinates of the inscribed circle: I[2; 1.79994708217]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.9155343162° = 167°54'55″ = 0.21109170508 rad
∠ B' = β' = 96.04223284191° = 96°2'32″ = 1.46553378014 rad
∠ C' = γ' = 96.04223284191° = 96°2'32″ = 1.46553378014 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 = 4 ; ; b = 19 ; ; c = 19 ; ;

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

p = a+b+c = 4+19+19 = 42 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 42 }{ 2 } = 21 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21 * (21-4)(21-19)(21-19) } ; ; T = sqrt{ 1428 } = 37.79 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 37.79 }{ 4 } = 18.89 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 37.79 }{ 19 } = 3.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 37.79 }{ 19 } = 3.98 ; ;

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{ 4**2-19**2-19**2 }{ 2 * 19 * 19 } ) = 12° 5'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-4**2-19**2 }{ 2 * 4 * 19 } ) = 83° 57'28" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-4**2-19**2 }{ 2 * 19 * 4 } ) = 83° 57'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 37.79 }{ 21 } = 1.8 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 12° 5'5" } = 9.55 ; ;




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