9 26 26 triangle

Acute isosceles triangle.

Sides: a = 9   b = 26   c = 26

Area: T = 115.2344272246
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 19.93435326005° = 19°56'1″ = 0.34879057754 rad
Angle ∠ B = β = 80.03332336998° = 80°2' = 1.39768434391 rad
Angle ∠ C = γ = 80.03332336998° = 80°2' = 1.39768434391 rad

Height: ha = 25.60876160546
Height: hb = 8.86441747881
Height: hc = 8.86441747881

Median: ma = 25.60876160546
Median: mb = 14.47441148261
Median: mc = 14.47441148261

Inradius: r = 3.77881728605
Circumradius: R = 13.19991982104

Vertex coordinates: A[26; 0] B[0; 0] C[1.55876923077; 8.86441747881]
Centroid: CG[9.18658974359; 2.95547249294]
Coordinates of the circumscribed circle: U[13; 2.28444766133]
Coordinates of the inscribed circle: I[4.5; 3.77881728605]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.06664674° = 160°3'59″ = 0.34879057754 rad
∠ B' = β' = 99.96767663002° = 99°58' = 1.39768434391 rad
∠ C' = γ' = 99.96767663002° = 99°58' = 1.39768434391 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 = 9 ; ; b = 26 ; ; c = 26 ; ;

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

p = a+b+c = 9+26+26 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-9)(30.5-26)(30.5-26) } ; ; T = sqrt{ 13278.94 } = 115.23 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 115.23 }{ 9 } = 25.61 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 115.23 }{ 26 } = 8.86 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 115.23 }{ 26 } = 8.86 ; ;

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{ 9**2-26**2-26**2 }{ 2 * 26 * 26 } ) = 19° 56'1" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-9**2-26**2 }{ 2 * 9 * 26 } ) = 80° 2' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-9**2-26**2 }{ 2 * 26 * 9 } ) = 80° 2' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 115.23 }{ 30.5 } = 3.78 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 19° 56'1" } = 13.2 ; ;




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