16 26 26 triangle

Acute isosceles triangle.

Sides: a = 16   b = 26   c = 26

Area: T = 197.909907003
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 35.84404262788° = 35°50'26″ = 0.62655334439 rad
Angle ∠ B = β = 72.08797868606° = 72°4'47″ = 1.25880296049 rad
Angle ∠ C = γ = 72.08797868606° = 72°4'47″ = 1.25880296049 rad

Height: ha = 24.73986337537
Height: hb = 15.22437746177
Height: hc = 15.22437746177

Median: ma = 24.73986337537
Median: mb = 17.23436879396
Median: mc = 17.23436879396

Inradius: r = 5.82108550009
Circumradius: R = 13.66328402104

Vertex coordinates: A[26; 0] B[0; 0] C[4.92330769231; 15.22437746177]
Centroid: CG[10.30876923077; 5.07545915392]
Coordinates of the circumscribed circle: U[13; 4.2043950834]
Coordinates of the inscribed circle: I[8; 5.82108550009]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.1659573721° = 144°9'34″ = 0.62655334439 rad
∠ B' = β' = 107.9220213139° = 107°55'13″ = 1.25880296049 rad
∠ C' = γ' = 107.9220213139° = 107°55'13″ = 1.25880296049 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 = 16 ; ; b = 26 ; ; c = 26 ; ;

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

p = a+b+c = 16+26+26 = 68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 68 }{ 2 } = 34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34 * (34-16)(34-26)(34-26) } ; ; T = sqrt{ 39168 } = 197.91 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 197.91 }{ 16 } = 24.74 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 197.91 }{ 26 } = 15.22 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 197.91 }{ 26 } = 15.22 ; ;

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{ 16**2-26**2-26**2 }{ 2 * 26 * 26 } ) = 35° 50'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-16**2-26**2 }{ 2 * 16 * 26 } ) = 72° 4'47" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-16**2-26**2 }{ 2 * 26 * 16 } ) = 72° 4'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 197.91 }{ 34 } = 5.82 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 35° 50'26" } = 13.66 ; ;




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