20 20 26 triangle

Acute isosceles triangle.

Sides: a = 20   b = 20   c = 26

Area: T = 197.5832893996
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 49.45883981265° = 49°27'30″ = 0.86332118901 rad
Angle ∠ B = β = 49.45883981265° = 49°27'30″ = 0.86332118901 rad
Angle ∠ C = γ = 81.0833203747° = 81°5' = 1.41551688735 rad

Height: ha = 19.75882893996
Height: hb = 19.75882893996
Height: hc = 15.19986841536

Median: ma = 20.92884495365
Median: mb = 20.92884495365
Median: mc = 15.19986841536

Inradius: r = 5.98773604241
Circumradius: R = 13.15990338992

Vertex coordinates: A[26; 0] B[0; 0] C[13; 15.19986841536]
Centroid: CG[13; 5.06662280512]
Coordinates of the circumscribed circle: U[13; 2.04396502544]
Coordinates of the inscribed circle: I[13; 5.98773604241]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.5421601874° = 130°32'30″ = 0.86332118901 rad
∠ B' = β' = 130.5421601874° = 130°32'30″ = 0.86332118901 rad
∠ C' = γ' = 98.9176796253° = 98°55' = 1.41551688735 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 = 20 ; ; b = 20 ; ; c = 26 ; ;

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

p = a+b+c = 20+20+26 = 66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 66 }{ 2 } = 33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33 * (33-20)(33-20)(33-26) } ; ; T = sqrt{ 39039 } = 197.58 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 197.58 }{ 20 } = 19.76 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 197.58 }{ 20 } = 19.76 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 197.58 }{ 26 } = 15.2 ; ;

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{ 20**2-20**2-26**2 }{ 2 * 20 * 26 } ) = 49° 27'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-20**2-26**2 }{ 2 * 20 * 26 } ) = 49° 27'30" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-20**2-20**2 }{ 2 * 20 * 20 } ) = 81° 5' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 197.58 }{ 33 } = 5.99 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 20 }{ 2 * sin 49° 27'30" } = 13.16 ; ;




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