26 30 30 triangle

Acute isosceles triangle.

Sides: a = 26   b = 30   c = 30

Area: T = 351.48111517
Perimeter: p = 86
Semiperimeter: s = 43

Angle ∠ A = α = 51.35985772389° = 51°21'31″ = 0.8966376272 rad
Angle ∠ B = β = 64.32107113805° = 64°19'15″ = 1.12326081908 rad
Angle ∠ C = γ = 64.32107113805° = 64°19'15″ = 1.12326081908 rad

Height: ha = 27.03770116692
Height: hb = 23.432207678
Height: hc = 23.432207678

Median: ma = 27.03770116692
Median: mb = 23.72876210354
Median: mc = 23.72876210354

Inradius: r = 8.17439802721
Circumradius: R = 16.64438512327

Vertex coordinates: A[30; 0] B[0; 0] C[11.26766666667; 23.432207678]
Centroid: CG[13.75655555556; 7.811069226]
Coordinates of the circumscribed circle: U[15; 7.21223355342]
Coordinates of the inscribed circle: I[13; 8.17439802721]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.6411422761° = 128°38'29″ = 0.8966376272 rad
∠ B' = β' = 115.6799288619° = 115°40'45″ = 1.12326081908 rad
∠ C' = γ' = 115.6799288619° = 115°40'45″ = 1.12326081908 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 = 30 ; ; c = 30 ; ;

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

p = a+b+c = 26+30+30 = 86 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 86 }{ 2 } = 43 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 43 * (43-26)(43-30)(43-30) } ; ; T = sqrt{ 123539 } = 351.48 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 351.48 }{ 26 } = 27.04 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 351.48 }{ 30 } = 23.43 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 351.48 }{ 30 } = 23.43 ; ;

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**2-30**2-30**2 }{ 2 * 30 * 30 } ) = 51° 21'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 30**2-26**2-30**2 }{ 2 * 26 * 30 } ) = 64° 19'15" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-26**2-30**2 }{ 2 * 30 * 26 } ) = 64° 19'15" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 351.48 }{ 43 } = 8.17 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 26 }{ 2 * sin 51° 21'31" } = 16.64 ; ;




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