1 20 20 triangle

Acute isosceles triangle.

Sides: a = 1   b = 20   c = 20

Area: T = 9.99768745116
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 2.86550874751° = 2°51'54″ = 0.05500052098 rad
Angle ∠ B = β = 88.56774562624° = 88°34'3″ = 1.54657937219 rad
Angle ∠ C = γ = 88.56774562624° = 88°34'3″ = 1.54657937219 rad

Height: ha = 19.99437490231
Height: hb = 10.9996874512
Height: hc = 10.9996874512

Median: ma = 19.99437490231
Median: mb = 10.02549688279
Median: mc = 10.02549688279

Inradius: r = 0.48876524152
Circumradius: R = 10.00331264656

Vertex coordinates: A[20; 0] B[0; 0] C[0.025; 10.9996874512]
Centroid: CG[6.675; 0.33332291504]
Coordinates of the circumscribed circle: U[10; 0.25500781616]
Coordinates of the inscribed circle: I[0.5; 0.48876524152]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 177.1354912525° = 177°8'6″ = 0.05500052098 rad
∠ B' = β' = 91.43325437376° = 91°25'57″ = 1.54657937219 rad
∠ C' = γ' = 91.43325437376° = 91°25'57″ = 1.54657937219 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 = 1 ; ; b = 20 ; ; c = 20 ; ;

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

p = a+b+c = 1+20+20 = 41 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 41 }{ 2 } = 20.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.5 * (20.5-1)(20.5-20)(20.5-20) } ; ; T = sqrt{ 99.94 } = 10 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 10 }{ 1 } = 19.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 10 }{ 20 } = 1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 10 }{ 20 } = 1 ; ;

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{ 1**2-20**2-20**2 }{ 2 * 20 * 20 } ) = 2° 51'54" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-1**2-20**2 }{ 2 * 1 * 20 } ) = 88° 34'3" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-1**2-20**2 }{ 2 * 20 * 1 } ) = 88° 34'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 10 }{ 20.5 } = 0.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1 }{ 2 * sin 2° 51'54" } = 10 ; ;




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