3 29 29 triangle

Acute isosceles triangle.

Sides: a = 3   b = 29   c = 29

Area: T = 43.44217713727
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 5.93297956944° = 5°55'47″ = 0.10334944588 rad
Angle ∠ B = β = 87.03551021528° = 87°2'6″ = 1.51990490974 rad
Angle ∠ C = γ = 87.03551021528° = 87°2'6″ = 1.51990490974 rad

Height: ha = 28.96111809151
Height: hb = 2.99659842326
Height: hc = 2.99659842326

Median: ma = 28.96111809151
Median: mb = 14.65443508898
Median: mc = 14.65443508898

Inradius: r = 1.42443203729
Circumradius: R = 14.51994355587

Vertex coordinates: A[29; 0] B[0; 0] C[0.15551724138; 2.99659842326]
Centroid: CG[9.71883908046; 0.99986614109]
Coordinates of the circumscribed circle: U[14.5; 0.75110052875]
Coordinates of the inscribed circle: I[1.5; 1.42443203729]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 174.0770204306° = 174°4'13″ = 0.10334944588 rad
∠ B' = β' = 92.96548978472° = 92°57'54″ = 1.51990490974 rad
∠ C' = γ' = 92.96548978472° = 92°57'54″ = 1.51990490974 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 = 29 ; ; c = 29 ; ;

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

p = a+b+c = 3+29+29 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-3)(30.5-29)(30.5-29) } ; ; T = sqrt{ 1887.19 } = 43.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 43.44 }{ 3 } = 28.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 43.44 }{ 29 } = 3 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 43.44 }{ 29 } = 3 ; ;

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**2-29**2-29**2 }{ 2 * 29 * 29 } ) = 5° 55'47" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-3**2-29**2 }{ 2 * 3 * 29 } ) = 87° 2'6" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-3**2-29**2 }{ 2 * 29 * 3 } ) = 87° 2'6" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 43.44 }{ 30.5 } = 1.42 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 5° 55'47" } = 14.52 ; ;




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