21 26 26 triangle

Acute isosceles triangle.

Sides: a = 21   b = 26   c = 26

Area: T = 249.7487747738
Perimeter: p = 73
Semiperimeter: s = 36.5

Angle ∠ A = α = 47.63876827869° = 47°38'16″ = 0.83114344127 rad
Angle ∠ B = β = 66.18111586065° = 66°10'52″ = 1.15550791205 rad
Angle ∠ C = γ = 66.18111586065° = 66°10'52″ = 1.15550791205 rad

Height: ha = 23.78554997845
Height: hb = 19.21113652106
Height: hc = 19.21113652106

Median: ma = 23.78554997845
Median: mb = 19.7365754356
Median: mc = 19.7365754356

Inradius: r = 6.84224040476
Circumradius: R = 14.211033836

Vertex coordinates: A[26; 0] B[0; 0] C[8.48107692308; 19.21113652106]
Centroid: CG[11.49435897436; 6.40437884035]
Coordinates of the circumscribed circle: U[13; 5.73987904915]
Coordinates of the inscribed circle: I[10.5; 6.84224040476]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.3622317213° = 132°21'44″ = 0.83114344127 rad
∠ B' = β' = 113.8198841393° = 113°49'8″ = 1.15550791205 rad
∠ C' = γ' = 113.8198841393° = 113°49'8″ = 1.15550791205 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 = 21 ; ; b = 26 ; ; c = 26 ; ;

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

p = a+b+c = 21+26+26 = 73 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 73 }{ 2 } = 36.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36.5 * (36.5-21)(36.5-26)(36.5-26) } ; ; T = sqrt{ 62373.94 } = 249.75 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 249.75 }{ 21 } = 23.79 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 249.75 }{ 26 } = 19.21 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 249.75 }{ 26 } = 19.21 ; ;

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{ 21**2-26**2-26**2 }{ 2 * 26 * 26 } ) = 47° 38'16" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-21**2-26**2 }{ 2 * 21 * 26 } ) = 66° 10'52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-21**2-26**2 }{ 2 * 26 * 21 } ) = 66° 10'52" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 249.75 }{ 36.5 } = 6.84 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 21 }{ 2 * sin 47° 38'16" } = 14.21 ; ;




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