26 29 29 triangle

Acute isosceles triangle.

Sides: a = 26   b = 29   c = 29

Area: T = 336.9998516317
Perimeter: p = 84
Semiperimeter: s = 42

Angle ∠ A = α = 53.26662374983° = 53°15'58″ = 0.93296712245 rad
Angle ∠ B = β = 63.36768812508° = 63°22'1″ = 1.10659607145 rad
Angle ∠ C = γ = 63.36768812508° = 63°22'1″ = 1.10659607145 rad

Height: ha = 25.92329627936
Height: hb = 23.24112769874
Height: hc = 23.24112769874

Median: ma = 25.92329627936
Median: mb = 23.41547389479
Median: mc = 23.41547389479

Inradius: r = 8.0243774198
Circumradius: R = 16.22111396648

Vertex coordinates: A[29; 0] B[0; 0] C[11.65551724138; 23.24112769874]
Centroid: CG[13.55217241379; 7.74770923291]
Coordinates of the circumscribed circle: U[14.5; 7.2721545367]
Coordinates of the inscribed circle: I[13; 8.0243774198]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 126.7343762502° = 126°44'2″ = 0.93296712245 rad
∠ B' = β' = 116.6333118749° = 116°37'59″ = 1.10659607145 rad
∠ C' = γ' = 116.6333118749° = 116°37'59″ = 1.10659607145 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 = 26 ; ; b = 29 ; ; c = 29 ; ;

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

p = a+b+c = 26+29+29 = 84 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 84 }{ 2 } = 42 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 42 * (42-26)(42-29)(42-29) } ; ; T = sqrt{ 113568 } = 337 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 337 }{ 26 } = 25.92 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 337 }{ 29 } = 23.24 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 337 }{ 29 } = 23.24 ; ;

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{ 26**2-29**2-29**2 }{ 2 * 29 * 29 } ) = 53° 15'58" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-26**2-29**2 }{ 2 * 26 * 29 } ) = 63° 22'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-26**2-29**2 }{ 2 * 29 * 26 } ) = 63° 22'1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 337 }{ 42 } = 8.02 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 26 }{ 2 * sin 53° 15'58" } = 16.22 ; ;




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