5 26 26 triangle

Acute isosceles triangle.

Sides: a = 5   b = 26   c = 26

Area: T = 64.6998821473
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 11.03554687476° = 11°2'8″ = 0.19326052641 rad
Angle ∠ B = β = 84.48222656262° = 84°28'56″ = 1.47444936947 rad
Angle ∠ C = γ = 84.48222656262° = 84°28'56″ = 1.47444936947 rad

Height: ha = 25.88795285892
Height: hb = 4.9776832421
Height: hc = 4.9776832421

Median: ma = 25.88795285892
Median: mb = 13.47221935853
Median: mc = 13.47221935853

Inradius: r = 2.27701340868
Circumradius: R = 13.06105161077

Vertex coordinates: A[26; 0] B[0; 0] C[0.48107692308; 4.9776832421]
Centroid: CG[8.82769230769; 1.65989441403]
Coordinates of the circumscribed circle: U[13; 1.25658188565]
Coordinates of the inscribed circle: I[2.5; 2.27701340868]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.9654531252° = 168°57'52″ = 0.19326052641 rad
∠ B' = β' = 95.51877343738° = 95°31'4″ = 1.47444936947 rad
∠ C' = γ' = 95.51877343738° = 95°31'4″ = 1.47444936947 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 = 5 ; ; b = 26 ; ; c = 26 ; ;

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

p = a+b+c = 5+26+26 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-5)(28.5-26)(28.5-26) } ; ; T = sqrt{ 4185.94 } = 64.7 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 64.7 }{ 5 } = 25.88 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 64.7 }{ 26 } = 4.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 64.7 }{ 26 } = 4.98 ; ;

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{ 5**2-26**2-26**2 }{ 2 * 26 * 26 } ) = 11° 2'8" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-5**2-26**2 }{ 2 * 5 * 26 } ) = 84° 28'56" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-5**2-26**2 }{ 2 * 26 * 5 } ) = 84° 28'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 64.7 }{ 28.5 } = 2.27 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 11° 2'8" } = 13.06 ; ;




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