25 26 26 triangle

Acute isosceles triangle.

Sides: a = 25   b = 26   c = 26

Area: T = 284.975532788
Perimeter: p = 77
Semiperimeter: s = 38.5

Angle ∠ A = α = 57.47113074898° = 57°28'17″ = 1.00330635411 rad
Angle ∠ B = β = 61.26443462551° = 61°15'52″ = 1.06992645562 rad
Angle ∠ C = γ = 61.26443462551° = 61°15'52″ = 1.06992645562 rad

Height: ha = 22.79880262304
Height: hb = 21.92111790677
Height: hc = 21.92111790677

Median: ma = 22.79880262304
Median: mb = 21.94331082575
Median: mc = 21.94331082575

Inradius: r = 7.40219565683
Circumradius: R = 14.82658448598

Vertex coordinates: A[26; 0] B[0; 0] C[12.01992307692; 21.92111790677]
Centroid: CG[12.67330769231; 7.30770596892]
Coordinates of the circumscribed circle: U[13; 7.12878100287]
Coordinates of the inscribed circle: I[12.5; 7.40219565683]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 122.529869251° = 122°31'43″ = 1.00330635411 rad
∠ B' = β' = 118.7365653745° = 118°44'8″ = 1.06992645562 rad
∠ C' = γ' = 118.7365653745° = 118°44'8″ = 1.06992645562 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 = 25 ; ; b = 26 ; ; c = 26 ; ;

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

p = a+b+c = 25+26+26 = 77 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 77 }{ 2 } = 38.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 38.5 * (38.5-25)(38.5-26)(38.5-26) } ; ; T = sqrt{ 81210.94 } = 284.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 284.98 }{ 25 } = 22.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 284.98 }{ 26 } = 21.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 284.98 }{ 26 } = 21.92 ; ;

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{ 25**2-26**2-26**2 }{ 2 * 26 * 26 } ) = 57° 28'17" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-25**2-26**2 }{ 2 * 25 * 26 } ) = 61° 15'52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-25**2-26**2 }{ 2 * 26 * 25 } ) = 61° 15'52" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 284.98 }{ 38.5 } = 7.4 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 25 }{ 2 * sin 57° 28'17" } = 14.83 ; ;




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