2 3 3 triangle

Acute isosceles triangle.

Sides: a = 2   b = 3   c = 3

Area: T = 2.82884271247
Perimeter: p = 8
Semiperimeter: s = 4

Angle ∠ A = α = 38.9422441269° = 38°56'33″ = 0.68796738189 rad
Angle ∠ B = β = 70.52987793655° = 70°31'44″ = 1.23109594173 rad
Angle ∠ C = γ = 70.52987793655° = 70°31'44″ = 1.23109594173 rad

Height: ha = 2.82884271247
Height: hb = 1.88656180832
Height: hc = 1.88656180832

Median: ma = 2.82884271247
Median: mb = 2.06215528128
Median: mc = 2.06215528128

Inradius: r = 0.70771067812
Circumradius: R = 1.59109902577

Vertex coordinates: A[3; 0] B[0; 0] C[0.66766666667; 1.88656180832]
Centroid: CG[1.22222222222; 0.62985393611]
Coordinates of the circumscribed circle: U[1.5; 0.53303300859]
Coordinates of the inscribed circle: I[1; 0.70771067812]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.0587558731° = 141°3'27″ = 0.68796738189 rad
∠ B' = β' = 109.4711220634° = 109°28'16″ = 1.23109594173 rad
∠ C' = γ' = 109.4711220634° = 109°28'16″ = 1.23109594173 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 = 3 ; ; c = 3 ; ;

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

p = a+b+c = 2+3+3 = 8 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 8 }{ 2 } = 4 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 4 * (4-2)(4-3)(4-3) } ; ; T = sqrt{ 8 } = 2.83 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2.83 }{ 2 } = 2.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2.83 }{ 3 } = 1.89 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2.83 }{ 3 } = 1.89 ; ;

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**2-3**2-3**2 }{ 2 * 3 * 3 } ) = 38° 56'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 3**2-2**2-3**2 }{ 2 * 2 * 3 } ) = 70° 31'44" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 3**2-2**2-3**2 }{ 2 * 3 * 2 } ) = 70° 31'44" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2.83 }{ 4 } = 0.71 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 38° 56'33" } = 1.59 ; ;




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