18 18 19 triangle

Acute isosceles triangle.

Sides: a = 18   b = 18   c = 19

Area: T = 145.2444406088
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 58.1454569176° = 58°8'40″ = 1.01548141743 rad
Angle ∠ B = β = 58.1454569176° = 58°8'40″ = 1.01548141743 rad
Angle ∠ C = γ = 63.71108616481° = 63°42'39″ = 1.1121964305 rad

Height: ha = 16.13882673432
Height: hb = 16.13882673432
Height: hc = 15.28988848514

Median: ma = 16.17109616288
Median: mb = 16.17109616288
Median: mc = 15.28988848514

Inradius: r = 5.28216147669
Circumradius: R = 10.59659330307

Vertex coordinates: A[19; 0] B[0; 0] C[9.5; 15.28988848514]
Centroid: CG[9.5; 5.09662949505]
Coordinates of the circumscribed circle: U[9.5; 4.69329518207]
Coordinates of the inscribed circle: I[9.5; 5.28216147669]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 121.8555430824° = 121°51'20″ = 1.01548141743 rad
∠ B' = β' = 121.8555430824° = 121°51'20″ = 1.01548141743 rad
∠ C' = γ' = 116.2899138352° = 116°17'21″ = 1.1121964305 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 = 18 ; ; c = 19 ; ;

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

p = a+b+c = 18+18+19 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-18)(27.5-18)(27.5-19) } ; ; T = sqrt{ 21095.94 } = 145.24 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 145.24 }{ 18 } = 16.14 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 145.24 }{ 18 } = 16.14 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 145.24 }{ 19 } = 15.29 ; ;

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**2-18**2-19**2 }{ 2 * 18 * 19 } ) = 58° 8'40" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-18**2-19**2 }{ 2 * 18 * 19 } ) = 58° 8'40" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-18**2-18**2 }{ 2 * 18 * 18 } ) = 63° 42'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 145.24 }{ 27.5 } = 5.28 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 58° 8'40" } = 10.6 ; ;




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