10 26 26 triangle

Acute isosceles triangle.

Sides: a = 10   b = 26   c = 26

Area: T = 127.5743508222
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 22.17549784219° = 22°10'30″ = 0.3877026385 rad
Angle ∠ B = β = 78.9132510789° = 78°54'45″ = 1.37772831343 rad
Angle ∠ C = γ = 78.9132510789° = 78°54'45″ = 1.37772831343 rad

Height: ha = 25.51547016443
Height: hb = 9.81333467863
Height: hc = 9.81333467863

Median: ma = 25.51547016443
Median: mb = 14.79986485869
Median: mc = 14.79986485869

Inradius: r = 4.11552744588
Circumradius: R = 13.24772644482

Vertex coordinates: A[26; 0] B[0; 0] C[1.92330769231; 9.81333467863]
Centroid: CG[9.30876923077; 3.27111155954]
Coordinates of the circumscribed circle: U[13; 2.54875508554]
Coordinates of the inscribed circle: I[5; 4.11552744588]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.8255021578° = 157°49'30″ = 0.3877026385 rad
∠ B' = β' = 101.0877489211° = 101°5'15″ = 1.37772831343 rad
∠ C' = γ' = 101.0877489211° = 101°5'15″ = 1.37772831343 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 = 10 ; ; b = 26 ; ; c = 26 ; ;

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

p = a+b+c = 10+26+26 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-10)(31-26)(31-26) } ; ; T = sqrt{ 16275 } = 127.57 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 127.57 }{ 10 } = 25.51 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 127.57 }{ 26 } = 9.81 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 127.57 }{ 26 } = 9.81 ; ;

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{ 10**2-26**2-26**2 }{ 2 * 26 * 26 } ) = 22° 10'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-10**2-26**2 }{ 2 * 10 * 26 } ) = 78° 54'45" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-10**2-26**2 }{ 2 * 26 * 10 } ) = 78° 54'45" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 127.57 }{ 31 } = 4.12 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 22° 10'30" } = 13.25 ; ;




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