1 29 29 triangle

Acute isosceles triangle.

Sides: a = 1   b = 29   c = 29

Area: T = 14.49878446674
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 1.97658144333° = 1°58'33″ = 0.03444844673 rad
Angle ∠ B = β = 89.01220927833° = 89°44″ = 1.55435540932 rad
Angle ∠ C = γ = 89.01220927833° = 89°44″ = 1.55435540932 rad

Height: ha = 28.99656893348
Height: hb = 10.9998513564
Height: hc = 10.9998513564

Median: ma = 28.99656893348
Median: mb = 14.5177231141
Median: mc = 14.5177231141

Inradius: r = 0.49114523616
Circumradius: R = 14.5022155653

Vertex coordinates: A[29; 0] B[0; 0] C[0.01772413793; 10.9998513564]
Centroid: CG[9.67224137931; 0.33332837855]
Coordinates of the circumscribed circle: U[14.5; 0.25500371664]
Coordinates of the inscribed circle: I[0.5; 0.49114523616]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 178.0244185567° = 178°1'27″ = 0.03444844673 rad
∠ B' = β' = 90.98879072167° = 90°59'16″ = 1.55435540932 rad
∠ C' = γ' = 90.98879072167° = 90°59'16″ = 1.55435540932 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 = 1 ; ; b = 29 ; ; c = 29 ; ;

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

p = a+b+c = 1+29+29 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-1)(29.5-29)(29.5-29) } ; ; T = sqrt{ 210.19 } = 14.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 14.5 }{ 1 } = 29 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 14.5 }{ 29 } = 1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 14.5 }{ 29 } = 1 ; ;

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{ 1**2-29**2-29**2 }{ 2 * 29 * 29 } ) = 1° 58'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-1**2-29**2 }{ 2 * 1 * 29 } ) = 89° 44" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-1**2-29**2 }{ 2 * 29 * 1 } ) = 89° 44" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 14.5 }{ 29.5 } = 0.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1 }{ 2 * sin 1° 58'33" } = 14.5 ; ;




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