3 20 20 triangle

Acute isosceles triangle.

Sides: a = 3   b = 20   c = 20

Area: T = 29.91655060128
Perimeter: p = 43
Semiperimeter: s = 21.5

Angle ∠ A = α = 8.60224446093° = 8°36'9″ = 0.15501409822 rad
Angle ∠ B = β = 85.69987776953° = 85°41'56″ = 1.49657258357 rad
Angle ∠ C = γ = 85.69987776953° = 85°41'56″ = 1.49657258357 rad

Height: ha = 19.94436706752
Height: hb = 2.99215506013
Height: hc = 2.99215506013

Median: ma = 19.94436706752
Median: mb = 10.22325241501
Median: mc = 10.22325241501

Inradius: r = 1.39114188843
Circumradius: R = 10.02882442113

Vertex coordinates: A[20; 0] B[0; 0] C[0.225; 2.99215506013]
Centroid: CG[6.74216666667; 0.99771835338]
Coordinates of the circumscribed circle: U[10; 0.75221183158]
Coordinates of the inscribed circle: I[1.5; 1.39114188843]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 171.3987555391° = 171°23'51″ = 0.15501409822 rad
∠ B' = β' = 94.30112223047° = 94°18'4″ = 1.49657258357 rad
∠ C' = γ' = 94.30112223047° = 94°18'4″ = 1.49657258357 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 = 3 ; ; b = 20 ; ; c = 20 ; ;

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

p = a+b+c = 3+20+20 = 43 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 43 }{ 2 } = 21.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21.5 * (21.5-3)(21.5-20)(21.5-20) } ; ; T = sqrt{ 894.94 } = 29.92 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 29.92 }{ 3 } = 19.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 29.92 }{ 20 } = 2.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 29.92 }{ 20 } = 2.99 ; ;

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{ 3**2-20**2-20**2 }{ 2 * 20 * 20 } ) = 8° 36'9" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-3**2-20**2 }{ 2 * 3 * 20 } ) = 85° 41'56" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-3**2-20**2 }{ 2 * 20 * 3 } ) = 85° 41'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 29.92 }{ 21.5 } = 1.39 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 8° 36'9" } = 10.03 ; ;




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