18 18 20 triangle

Acute isosceles triangle.

Sides: a = 18   b = 18   c = 20

Area: T = 149.6666295471
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 56.25110114041° = 56°15'4″ = 0.98217653566 rad
Angle ∠ B = β = 56.25110114041° = 56°15'4″ = 0.98217653566 rad
Angle ∠ C = γ = 67.49879771918° = 67°29'53″ = 1.17880619404 rad

Height: ha = 16.63295883857
Height: hb = 16.63295883857
Height: hc = 14.96766295471

Median: ma = 16.76330546142
Median: mb = 16.76330546142
Median: mc = 14.96766295471

Inradius: r = 5.34552248382
Circumradius: R = 10.82440802975

Vertex coordinates: A[20; 0] B[0; 0] C[10; 14.96766295471]
Centroid: CG[10; 4.98988765157]
Coordinates of the circumscribed circle: U[10; 4.14325492496]
Coordinates of the inscribed circle: I[10; 5.34552248382]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 123.7498988596° = 123°44'56″ = 0.98217653566 rad
∠ B' = β' = 123.7498988596° = 123°44'56″ = 0.98217653566 rad
∠ C' = γ' = 112.5022022808° = 112°30'7″ = 1.17880619404 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 = 20 ; ;

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

p = a+b+c = 18+18+20 = 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)(28-18)(28-20) } ; ; T = sqrt{ 22400 } = 149.67 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 149.67 }{ 18 } = 16.63 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 149.67 }{ 18 } = 16.63 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 149.67 }{ 20 } = 14.97 ; ;

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**2-20**2 }{ 2 * 18 * 20 } ) = 56° 15'4" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-18**2-20**2 }{ 2 * 18 * 20 } ) = 56° 15'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-18**2-18**2 }{ 2 * 18 * 18 } ) = 67° 29'53" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 149.67 }{ 28 } = 5.35 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 56° 15'4" } = 10.82 ; ;




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