19 26 26 triangle

Acute isosceles triangle.

Sides: a = 19   b = 26   c = 26

Area: T = 229.9221589895
Perimeter: p = 71
Semiperimeter: s = 35.5

Angle ∠ A = α = 42.86325090077° = 42°51'45″ = 0.74880919078 rad
Angle ∠ B = β = 68.56987454962° = 68°34'7″ = 1.19767503729 rad
Angle ∠ C = γ = 68.56987454962° = 68°34'7″ = 1.19767503729 rad

Height: ha = 24.20222726206
Height: hb = 17.68662761458
Height: hc = 17.68662761458

Median: ma = 24.20222726206
Median: mb = 18.69549190958
Median: mc = 18.69549190958

Inradius: r = 6.47766645041
Circumradius: R = 13.96656306372

Vertex coordinates: A[26; 0] B[0; 0] C[6.94223076923; 17.68662761458]
Centroid: CG[10.98107692308; 5.89554253819]
Coordinates of the circumscribed circle: U[13; 5.1032826579]
Coordinates of the inscribed circle: I[9.5; 6.47766645041]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.1377490992° = 137°8'15″ = 0.74880919078 rad
∠ B' = β' = 111.4311254504° = 111°25'53″ = 1.19767503729 rad
∠ C' = γ' = 111.4311254504° = 111°25'53″ = 1.19767503729 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 = 19 ; ; b = 26 ; ; c = 26 ; ;

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

p = a+b+c = 19+26+26 = 71 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 71 }{ 2 } = 35.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35.5 * (35.5-19)(35.5-26)(35.5-26) } ; ; T = sqrt{ 52863.94 } = 229.92 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 229.92 }{ 19 } = 24.2 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 229.92 }{ 26 } = 17.69 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 229.92 }{ 26 } = 17.69 ; ;

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{ 19**2-26**2-26**2 }{ 2 * 26 * 26 } ) = 42° 51'45" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-19**2-26**2 }{ 2 * 19 * 26 } ) = 68° 34'7" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-19**2-26**2 }{ 2 * 26 * 19 } ) = 68° 34'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 229.92 }{ 35.5 } = 6.48 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 42° 51'45" } = 13.97 ; ;




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