2 2 3 triangle

Obtuse isosceles triangle.

Sides: a = 2   b = 2   c = 3

Area: T = 1.98443134833
Perimeter: p = 7
Semiperimeter: s = 3.5

Angle ∠ A = α = 41.41096221093° = 41°24'35″ = 0.72327342478 rad
Angle ∠ B = β = 41.41096221093° = 41°24'35″ = 0.72327342478 rad
Angle ∠ C = γ = 97.18107557815° = 97°10'51″ = 1.6966124158 rad

Height: ha = 1.98443134833
Height: hb = 1.98443134833
Height: hc = 1.32328756555

Median: ma = 2.34552078799
Median: mb = 2.34552078799
Median: mc = 1.32328756555

Inradius: r = 0.56769467095
Circumradius: R = 1.5121857892

Vertex coordinates: A[3; 0] B[0; 0] C[1.5; 1.32328756555]
Centroid: CG[1.5; 0.44109585518]
Coordinates of the circumscribed circle: U[1.5; -0.18989822365]
Coordinates of the inscribed circle: I[1.5; 0.56769467095]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.5990377891° = 138°35'25″ = 0.72327342478 rad
∠ B' = β' = 138.5990377891° = 138°35'25″ = 0.72327342478 rad
∠ C' = γ' = 82.81992442185° = 82°49'9″ = 1.6966124158 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 = 2 ; ; b = 2 ; ; c = 3 ; ;

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

p = a+b+c = 2+2+3 = 7 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 7 }{ 2 } = 3.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 3.5 * (3.5-2)(3.5-2)(3.5-3) } ; ; T = sqrt{ 3.94 } = 1.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.98 }{ 2 } = 1.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.98 }{ 2 } = 1.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.98 }{ 3 } = 1.32 ; ;

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{ 2**2-2**2-3**2 }{ 2 * 2 * 3 } ) = 41° 24'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 2**2-2**2-3**2 }{ 2 * 2 * 3 } ) = 41° 24'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 3**2-2**2-2**2 }{ 2 * 2 * 2 } ) = 97° 10'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.98 }{ 3.5 } = 0.57 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 41° 24'35" } = 1.51 ; ;




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