4.5 3.36 3.36 triangle

Acute isosceles triangle.

Sides: a = 4.5   b = 3.36   c = 3.36

Area: T = 5.61546855433
Perimeter: p = 11.22
Semiperimeter: s = 5.61

Angle ∠ A = α = 84.07990126579° = 84°4'44″ = 1.46774556027 rad
Angle ∠ B = β = 47.9660493671° = 47°57'38″ = 0.83770685254 rad
Angle ∠ C = γ = 47.9660493671° = 47°57'38″ = 0.83770685254 rad

Height: ha = 2.4955415797
Height: hb = 3.34220747281
Height: hc = 3.34220747281

Median: ma = 2.4955415797
Median: mb = 3.59882495744
Median: mc = 3.59882495744

Inradius: r = 1.00108352127
Circumradius: R = 2.26220679114

Vertex coordinates: A[3.36; 0] B[0; 0] C[3.01333928571; 3.34220747281]
Centroid: CG[2.12444642857; 1.11440249094]
Coordinates of the circumscribed circle: U[1.68; 1.51547776192]
Coordinates of the inscribed circle: I[2.25; 1.00108352127]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 95.92109873421° = 95°55'16″ = 1.46774556027 rad
∠ B' = β' = 132.0439506329° = 132°2'22″ = 0.83770685254 rad
∠ C' = γ' = 132.0439506329° = 132°2'22″ = 0.83770685254 rad

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How did we calculate this triangle?

a = 4.5 ; ; b = 3.36 ; ; c = 3.36 ; ;

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

p = a+b+c = 4.5+3.36+3.36 = 11.22 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 11.22 }{ 2 } = 5.61 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 5.61 * (5.61-4.5)(5.61-3.36)(5.61-3.36) } ; ; T = sqrt{ 31.52 } = 5.61 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5.61 }{ 4.5 } = 2.5 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5.61 }{ 3.36 } = 3.34 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5.61 }{ 3.36 } = 3.34 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 3.36**2+3.36**2-4.5**2 }{ 2 * 3.36 * 3.36 } ) = 84° 4'44" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 4.5**2+3.36**2-3.36**2 }{ 2 * 4.5 * 3.36 } ) = 47° 57'38" ; ; gamma = 180° - alpha - beta = 180° - 84° 4'44" - 47° 57'38" = 47° 57'38" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5.61 }{ 5.61 } = 1 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 4.5 }{ 2 * sin 84° 4'44" } = 2.26 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.36**2+2 * 3.36**2 - 4.5**2 } }{ 2 } = 2.495 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.36**2+2 * 4.5**2 - 3.36**2 } }{ 2 } = 3.598 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.36**2+2 * 4.5**2 - 3.36**2 } }{ 2 } = 3.598 ; ;
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