4 26 26 triangle

Acute isosceles triangle.

Sides: a = 4   b = 26   c = 26

Area: T = 51.84659255873
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 8.82334515715° = 8°49'24″ = 0.15439982813 rad
Angle ∠ B = β = 85.58882742142° = 85°35'18″ = 1.49437971861 rad
Angle ∠ C = γ = 85.58882742142° = 85°35'18″ = 1.49437971861 rad

Height: ha = 25.92329627936
Height: hb = 3.98881481221
Height: hc = 3.98881481221

Median: ma = 25.92329627936
Median: mb = 13.30441346957
Median: mc = 13.30441346957

Inradius: r = 1.85216401995
Circumradius: R = 13.03986330718

Vertex coordinates: A[26; 0] B[0; 0] C[0.30876923077; 3.98881481221]
Centroid: CG[8.76992307692; 1.32993827074]
Coordinates of the circumscribed circle: U[13; 1.00329717748]
Coordinates of the inscribed circle: I[2; 1.85216401995]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 171.1776548428° = 171°10'36″ = 0.15439982813 rad
∠ B' = β' = 94.41217257858° = 94°24'42″ = 1.49437971861 rad
∠ C' = γ' = 94.41217257858° = 94°24'42″ = 1.49437971861 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 = 4 ; ; b = 26 ; ; c = 26 ; ;

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

p = a+b+c = 4+26+26 = 56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 56 }{ 2 } = 28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28 * (28-4)(28-26)(28-26) } ; ; T = sqrt{ 2688 } = 51.85 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 51.85 }{ 4 } = 25.92 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 51.85 }{ 26 } = 3.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 51.85 }{ 26 } = 3.99 ; ;

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{ 4**2-26**2-26**2 }{ 2 * 26 * 26 } ) = 8° 49'24" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-4**2-26**2 }{ 2 * 4 * 26 } ) = 85° 35'18" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-4**2-26**2 }{ 2 * 26 * 4 } ) = 85° 35'18" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 51.85 }{ 28 } = 1.85 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 8° 49'24" } = 13.04 ; ;




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