11 26 26 triangle

Acute isosceles triangle.

Sides: a = 11   b = 26   c = 26

Area: T = 139.7643863355
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 24.42550505378° = 24°25'30″ = 0.42662975519 rad
Angle ∠ B = β = 77.78774747311° = 77°47'15″ = 1.35876475509 rad
Angle ∠ C = γ = 77.78774747311° = 77°47'15″ = 1.35876475509 rad

Height: ha = 25.41216115191
Height: hb = 10.75110664119
Height: hc = 10.75110664119

Median: ma = 25.41216115191
Median: mb = 15.14992574075
Median: mc = 15.14992574075

Inradius: r = 4.4376948043
Circumradius: R = 13.30110061068

Vertex coordinates: A[26; 0] B[0; 0] C[2.32769230769; 10.75110664119]
Centroid: CG[9.44223076923; 3.5843688804]
Coordinates of the circumscribed circle: U[13; 2.81436743687]
Coordinates of the inscribed circle: I[5.5; 4.4376948043]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.5754949462° = 155°34'30″ = 0.42662975519 rad
∠ B' = β' = 102.2132525269° = 102°12'45″ = 1.35876475509 rad
∠ C' = γ' = 102.2132525269° = 102°12'45″ = 1.35876475509 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 = 11 ; ; b = 26 ; ; c = 26 ; ;

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

p = a+b+c = 11+26+26 = 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 * (31.5-11)(31.5-26)(31.5-26) } ; ; T = sqrt{ 19533.94 } = 139.76 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 139.76 }{ 11 } = 25.41 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 139.76 }{ 26 } = 10.75 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 139.76 }{ 26 } = 10.75 ; ;

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{ 11**2-26**2-26**2 }{ 2 * 26 * 26 } ) = 24° 25'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-11**2-26**2 }{ 2 * 11 * 26 } ) = 77° 47'15" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-11**2-26**2 }{ 2 * 26 * 11 } ) = 77° 47'15" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 139.76 }{ 31.5 } = 4.44 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 24° 25'30" } = 13.3 ; ;




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