3 4 4 triangle

Acute isosceles triangle.

Sides: a = 3   b = 4   c = 4

Area: T = 5.56221488653
Perimeter: p = 11
Semiperimeter: s = 5.5

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

Height: ha = 3.70880992435
Height: hb = 2.78110744327
Height: hc = 2.78110744327

Median: ma = 3.70880992435
Median: mb = 2.91554759474
Median: mc = 2.91554759474

Inradius: r = 1.01112997937
Circumradius: R = 2.15774395599

Vertex coordinates: A[4; 0] B[0; 0] C[1.125; 2.78110744327]
Centroid: CG[1.70883333333; 0.92770248109]
Coordinates of the circumscribed circle: U[2; 0.8099039835]
Coordinates of the inscribed circle: I[1.5; 1.01112997937]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.9511374326° = 135°57'5″ = 0.7698793549 rad
∠ B' = β' = 112.0244312837° = 112°1'28″ = 1.18663995523 rad
∠ C' = γ' = 112.0244312837° = 112°1'28″ = 1.18663995523 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 = 3 ; ; b = 4 ; ; c = 4 ; ;

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

p = a+b+c = 3+4+4 = 11 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 11 }{ 2 } = 5.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 5.5 * (5.5-3)(5.5-4)(5.5-4) } ; ; T = sqrt{ 30.94 } = 5.56 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5.56 }{ 3 } = 3.71 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5.56 }{ 4 } = 2.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5.56 }{ 4 } = 2.78 ; ;

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{ 3**2-4**2-4**2 }{ 2 * 4 * 4 } ) = 44° 2'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4**2-3**2-4**2 }{ 2 * 3 * 4 } ) = 67° 58'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 4**2-3**2-4**2 }{ 2 * 4 * 3 } ) = 67° 58'32" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5.56 }{ 5.5 } = 1.01 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 44° 2'55" } = 2.16 ; ;




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