21 21 26 triangle

Acute isosceles triangle.

Sides: a = 21   b = 21   c = 26

Area: T = 214.4011492532
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 51.75333801217° = 51°45'12″ = 0.90332668822 rad
Angle ∠ B = β = 51.75333801217° = 51°45'12″ = 0.90332668822 rad
Angle ∠ C = γ = 76.49332397567° = 76°29'36″ = 1.33550588893 rad

Height: ha = 20.4199189765
Height: hb = 20.4199189765
Height: hc = 16.49224225025

Median: ma = 21.17219153597
Median: mb = 21.17219153597
Median: mc = 16.49224225025

Inradius: r = 6.30659262509
Circumradius: R = 13.37697763301

Vertex coordinates: A[26; 0] B[0; 0] C[13; 16.49224225025]
Centroid: CG[13; 5.49774741675]
Coordinates of the circumscribed circle: U[13; 3.12326461723]
Coordinates of the inscribed circle: I[13; 6.30659262509]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.2476619878° = 128°14'48″ = 0.90332668822 rad
∠ B' = β' = 128.2476619878° = 128°14'48″ = 0.90332668822 rad
∠ C' = γ' = 103.5076760243° = 103°30'24″ = 1.33550588893 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 = 21 ; ; c = 26 ; ;

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

p = a+b+c = 21+21+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 * (34-21)(34-21)(34-26) } ; ; T = sqrt{ 45968 } = 214.4 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 214.4 }{ 21 } = 20.42 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 214.4 }{ 21 } = 20.42 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 214.4 }{ 26 } = 16.49 ; ;

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**2-21**2-26**2 }{ 2 * 21 * 26 } ) = 51° 45'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-21**2-26**2 }{ 2 * 21 * 26 } ) = 51° 45'12" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-21**2-21**2 }{ 2 * 21 * 21 } ) = 76° 29'36" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 214.4 }{ 34 } = 6.31 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 21 }{ 2 * sin 51° 45'12" } = 13.37 ; ;




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