18 19 19 triangle

Acute isosceles triangle.

Sides: a = 18   b = 19   c = 19

Area: T = 150.5998804776
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 56.54774272627° = 56°32'51″ = 0.98769387893 rad
Angle ∠ B = β = 61.72662863686° = 61°43'35″ = 1.07773269322 rad
Angle ∠ C = γ = 61.72662863686° = 61°43'35″ = 1.07773269322 rad

Height: ha = 16.73332005307
Height: hb = 15.85325057659
Height: hc = 15.85325057659

Median: ma = 16.73332005307
Median: mb = 15.88223801743
Median: mc = 15.88223801743

Inradius: r = 5.3798528742
Circumradius: R = 10.78769381992

Vertex coordinates: A[19; 0] B[0; 0] C[8.52663157895; 15.85325057659]
Centroid: CG[9.17554385965; 5.28441685886]
Coordinates of the circumscribed circle: U[9.5; 5.11096023049]
Coordinates of the inscribed circle: I[9; 5.3798528742]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 123.4532572737° = 123°27'9″ = 0.98769387893 rad
∠ B' = β' = 118.2743713631° = 118°16'25″ = 1.07773269322 rad
∠ C' = γ' = 118.2743713631° = 118°16'25″ = 1.07773269322 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 = 18 ; ; b = 19 ; ; c = 19 ; ;

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

p = a+b+c = 18+19+19 = 56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 56 }{ 2 } = 28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28 * (28-18)(28-19)(28-19) } ; ; T = sqrt{ 22680 } = 150.6 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 150.6 }{ 18 } = 16.73 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 150.6 }{ 19 } = 15.85 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 150.6 }{ 19 } = 15.85 ; ;

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{ 18**2-19**2-19**2 }{ 2 * 19 * 19 } ) = 56° 32'51" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-18**2-19**2 }{ 2 * 18 * 19 } ) = 61° 43'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-18**2-19**2 }{ 2 * 19 * 18 } ) = 61° 43'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 150.6 }{ 28 } = 5.38 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 56° 32'51" } = 10.79 ; ;




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