26 26 30 triangle

Acute isosceles triangle.

Sides: a = 26   b = 26   c = 30

Area: T = 318.5511408724
Perimeter: p = 82
Semiperimeter: s = 41

Angle ∠ A = α = 54.76655820154° = 54°45'56″ = 0.95658397229 rad
Angle ∠ B = β = 54.76655820154° = 54°45'56″ = 0.95658397229 rad
Angle ∠ C = γ = 70.46988359692° = 70°28'8″ = 1.23299132077 rad

Height: ha = 24.50439545172
Height: hb = 24.50439545172
Height: hc = 21.23767605816

Median: ma = 24.88797106092
Median: mb = 24.88797106092
Median: mc = 21.23767605816

Inradius: r = 7.77695465542
Circumradius: R = 15.9165798396

Vertex coordinates: A[30; 0] B[0; 0] C[15; 21.23767605816]
Centroid: CG[15; 7.07989201939]
Coordinates of the circumscribed circle: U[15; 5.32109621856]
Coordinates of the inscribed circle: I[15; 7.77695465542]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.2344417985° = 125°14'4″ = 0.95658397229 rad
∠ B' = β' = 125.2344417985° = 125°14'4″ = 0.95658397229 rad
∠ C' = γ' = 109.5311164031° = 109°31'52″ = 1.23299132077 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 = 26 ; ; b = 26 ; ; c = 30 ; ;

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

p = a+b+c = 26+26+30 = 82 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 82 }{ 2 } = 41 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 41 * (41-26)(41-26)(41-30) } ; ; T = sqrt{ 101475 } = 318.55 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 318.55 }{ 26 } = 24.5 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 318.55 }{ 26 } = 24.5 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 318.55 }{ 30 } = 21.24 ; ;

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{ 26**2-26**2-30**2 }{ 2 * 26 * 30 } ) = 54° 45'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-26**2-30**2 }{ 2 * 26 * 30 } ) = 54° 45'56" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-26**2-26**2 }{ 2 * 26 * 26 } ) = 70° 28'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 318.55 }{ 41 } = 7.77 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 26 }{ 2 * sin 54° 45'56" } = 15.92 ; ;




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