17 26 26 triangle

Acute isosceles triangle.

Sides: a = 17   b = 26   c = 26

Area: T = 208.856626038
Perimeter: p = 69
Semiperimeter: s = 34.5

Angle ∠ A = α = 38.16442496072° = 38°9'51″ = 0.66660918122 rad
Angle ∠ B = β = 70.91878751964° = 70°55'4″ = 1.23877504207 rad
Angle ∠ C = γ = 70.91878751964° = 70°55'4″ = 1.23877504207 rad

Height: ha = 24.57113247506
Height: hb = 16.06658661831
Height: hc = 16.06658661831

Median: ma = 24.57113247506
Median: mb = 17.70659312096
Median: mc = 17.70659312096

Inradius: r = 6.05438046487
Circumradius: R = 13.75658720757

Vertex coordinates: A[26; 0] B[0; 0] C[5.55876923077; 16.06658661831]
Centroid: CG[10.51992307692; 5.35552887277]
Coordinates of the circumscribed circle: U[13; 4.49771120247]
Coordinates of the inscribed circle: I[8.5; 6.05438046487]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.8365750393° = 141°50'9″ = 0.66660918122 rad
∠ B' = β' = 109.0822124804° = 109°4'56″ = 1.23877504207 rad
∠ C' = γ' = 109.0822124804° = 109°4'56″ = 1.23877504207 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 = 17 ; ; b = 26 ; ; c = 26 ; ;

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

p = a+b+c = 17+26+26 = 69 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 69 }{ 2 } = 34.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34.5 * (34.5-17)(34.5-26)(34.5-26) } ; ; T = sqrt{ 43620.94 } = 208.86 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 208.86 }{ 17 } = 24.57 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 208.86 }{ 26 } = 16.07 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 208.86 }{ 26 } = 16.07 ; ;

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{ 17**2-26**2-26**2 }{ 2 * 26 * 26 } ) = 38° 9'51" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-17**2-26**2 }{ 2 * 17 * 26 } ) = 70° 55'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-17**2-26**2 }{ 2 * 26 * 17 } ) = 70° 55'4" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 208.86 }{ 34.5 } = 6.05 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 38° 9'51" } = 13.76 ; ;




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