5 29 29 triangle

Acute isosceles triangle.

Sides: a = 5   b = 29   c = 29

Area: T = 72.2330101066
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 9.89108594358° = 9°53'27″ = 0.1732628063 rad
Angle ∠ B = β = 85.05545702821° = 85°3'16″ = 1.48444822953 rad
Angle ∠ C = γ = 85.05545702821° = 85°3'16″ = 1.48444822953 rad

Height: ha = 28.89220404264
Height: hb = 4.98113862804
Height: hc = 4.98113862804

Median: ma = 28.89220404264
Median: mb = 14.92548115566
Median: mc = 14.92548115566

Inradius: r = 2.29330190815
Circumradius: R = 14.55441814906

Vertex coordinates: A[29; 0] B[0; 0] C[0.43110344828; 4.98113862804]
Centroid: CG[9.81103448276; 1.66604620935]
Coordinates of the circumscribed circle: U[14.5; 1.25546708182]
Coordinates of the inscribed circle: I[2.5; 2.29330190815]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.1099140564° = 170°6'33″ = 0.1732628063 rad
∠ B' = β' = 94.94554297179° = 94°56'44″ = 1.48444822953 rad
∠ C' = γ' = 94.94554297179° = 94°56'44″ = 1.48444822953 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 = 5 ; ; b = 29 ; ; c = 29 ; ;

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

p = a+b+c = 5+29+29 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-5)(31.5-29)(31.5-29) } ; ; T = sqrt{ 5217.19 } = 72.23 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 72.23 }{ 5 } = 28.89 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 72.23 }{ 29 } = 4.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 72.23 }{ 29 } = 4.98 ; ;

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{ 5**2-29**2-29**2 }{ 2 * 29 * 29 } ) = 9° 53'27" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-5**2-29**2 }{ 2 * 5 * 29 } ) = 85° 3'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-5**2-29**2 }{ 2 * 29 * 5 } ) = 85° 3'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 72.23 }{ 31.5 } = 2.29 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 9° 53'27" } = 14.55 ; ;




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