8 20 20 triangle

Acute isosceles triangle.

Sides: a = 8   b = 20   c = 20

Area: T = 78.38436717691
Perimeter: p = 48
Semiperimeter: s = 24

Angle ∠ A = α = 23.07439180656° = 23°4'26″ = 0.40327158416 rad
Angle ∠ B = β = 78.46330409672° = 78°27'47″ = 1.3699438406 rad
Angle ∠ C = γ = 78.46330409672° = 78°27'47″ = 1.3699438406 rad

Height: ha = 19.59659179423
Height: hb = 7.83883671769
Height: hc = 7.83883671769

Median: ma = 19.59659179423
Median: mb = 11.48991252931
Median: mc = 11.48991252931

Inradius: r = 3.26659863237
Circumradius: R = 10.20662072616

Vertex coordinates: A[20; 0] B[0; 0] C[1.6; 7.83883671769]
Centroid: CG[7.2; 2.6132789059]
Coordinates of the circumscribed circle: U[10; 2.04112414523]
Coordinates of the inscribed circle: I[4; 3.26659863237]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.9266081934° = 156°55'34″ = 0.40327158416 rad
∠ B' = β' = 101.5376959033° = 101°32'13″ = 1.3699438406 rad
∠ C' = γ' = 101.5376959033° = 101°32'13″ = 1.3699438406 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 = 8 ; ; b = 20 ; ; c = 20 ; ;

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

p = a+b+c = 8+20+20 = 48 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 48 }{ 2 } = 24 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24 * (24-8)(24-20)(24-20) } ; ; T = sqrt{ 6144 } = 78.38 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 78.38 }{ 8 } = 19.6 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 78.38 }{ 20 } = 7.84 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 78.38 }{ 20 } = 7.84 ; ;

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{ 8**2-20**2-20**2 }{ 2 * 20 * 20 } ) = 23° 4'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-8**2-20**2 }{ 2 * 8 * 20 } ) = 78° 27'47" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-8**2-20**2 }{ 2 * 20 * 8 } ) = 78° 27'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 78.38 }{ 24 } = 3.27 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 23° 4'26" } = 10.21 ; ;




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