3 26 26 triangle

Acute isosceles triangle.

Sides: a = 3   b = 26   c = 26

Area: T = 38.93550420573
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 6.61547243593° = 6°36'53″ = 0.11554487192 rad
Angle ∠ B = β = 86.69326378203° = 86°41'34″ = 1.51330719672 rad
Angle ∠ C = γ = 86.69326378203° = 86°41'34″ = 1.51330719672 rad

Height: ha = 25.95766947048
Height: hb = 2.99550032352
Height: hc = 2.99550032352

Median: ma = 25.95766947048
Median: mb = 13.17219398723
Median: mc = 13.17219398723

Inradius: r = 1.41658197112
Circumradius: R = 13.02216887721

Vertex coordinates: A[26; 0] B[0; 0] C[0.17330769231; 2.99550032352]
Centroid: CG[8.72443589744; 0.99883344117]
Coordinates of the circumscribed circle: U[13; 0.75112512753]
Coordinates of the inscribed circle: I[1.5; 1.41658197112]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 173.3855275641° = 173°23'7″ = 0.11554487192 rad
∠ B' = β' = 93.30773621797° = 93°18'26″ = 1.51330719672 rad
∠ C' = γ' = 93.30773621797° = 93°18'26″ = 1.51330719672 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 = 26 ; ; c = 26 ; ;

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

p = a+b+c = 3+26+26 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-3)(27.5-26)(27.5-26) } ; ; T = sqrt{ 1515.94 } = 38.94 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 38.94 }{ 3 } = 25.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 38.94 }{ 26 } = 3 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 38.94 }{ 26 } = 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**2-26**2-26**2 }{ 2 * 26 * 26 } ) = 6° 36'53" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-3**2-26**2 }{ 2 * 3 * 26 } ) = 86° 41'34" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-3**2-26**2 }{ 2 * 26 * 3 } ) = 86° 41'34" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 38.94 }{ 27.5 } = 1.42 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 6° 36'53" } = 13.02 ; ;




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