1.2 1.2 0.9 triangle

Acute isosceles triangle.

Sides: a = 1.2   b = 1.2   c = 0.9

Area: T = 0.50105933979
Perimeter: p = 3.3
Semiperimeter: s = 1.65

Angle ∠ A = α = 67.9765687163° = 67°58'32″ = 1.18663995523 rad
Angle ∠ B = β = 67.9765687163° = 67°58'32″ = 1.18663995523 rad
Angle ∠ C = γ = 44.04986256741° = 44°2'55″ = 0.7698793549 rad

Height: ha = 0.83443223298
Height: hb = 0.83443223298
Height: hc = 1.11224297731

Median: ma = 0.87546427842
Median: mb = 0.87546427842
Median: mc = 1.11224297731

Inradius: r = 0.30333899381
Circumradius: R = 0.6477231868

Vertex coordinates: A[0.9; 0] B[0; 0] C[0.45; 1.11224297731]
Centroid: CG[0.45; 0.37108099244]
Coordinates of the circumscribed circle: U[0.45; 0.46551979051]
Coordinates of the inscribed circle: I[0.45; 0.30333899381]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 112.0244312837° = 112°1'28″ = 1.18663995523 rad
∠ B' = β' = 112.0244312837° = 112°1'28″ = 1.18663995523 rad
∠ C' = γ' = 135.9511374326° = 135°57'5″ = 0.7698793549 rad

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How did we calculate this triangle?

a = 1.2 ; ; b = 1.2 ; ; c = 0.9 ; ;

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

p = a+b+c = 1.2+1.2+0.9 = 3.3 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 3.3 }{ 2 } = 1.65 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1.65 * (1.65-1.2)(1.65-1.2)(1.65-0.9) } ; ; T = sqrt{ 0.25 } = 0.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.5 }{ 1.2 } = 0.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.5 }{ 1.2 } = 0.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.5 }{ 0.9 } = 1.11 ; ;

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{ 1.2**2-1.2**2-0.9**2 }{ 2 * 1.2 * 0.9 } ) = 67° 58'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 1.2**2-1.2**2-0.9**2 }{ 2 * 1.2 * 0.9 } ) = 67° 58'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 0.9**2-1.2**2-1.2**2 }{ 2 * 1.2 * 1.2 } ) = 44° 2'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.5 }{ 1.65 } = 0.3 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1.2 }{ 2 * sin 67° 58'32" } = 0.65 ; ;




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