6 20 20 triangle

Acute isosceles triangle.

Sides: a = 6   b = 20   c = 20

Area: T = 59.32111597999
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 17.25438531174° = 17°15'14″ = 0.30111365456 rad
Angle ∠ B = β = 81.37330734413° = 81°22'23″ = 1.4220228054 rad
Angle ∠ C = γ = 81.37330734413° = 81°22'23″ = 1.4220228054 rad

Height: ha = 19.77437199333
Height: hb = 5.932211598
Height: hc = 5.932211598

Median: ma = 19.77437199333
Median: mb = 10.86327804912
Median: mc = 10.86327804912

Inradius: r = 2.57991808609
Circumradius: R = 10.11444347485

Vertex coordinates: A[20; 0] B[0; 0] C[0.9; 5.932211598]
Centroid: CG[6.96766666667; 1.97773719933]
Coordinates of the circumscribed circle: U[10; 1.51771652123]
Coordinates of the inscribed circle: I[3; 2.57991808609]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.7466146883° = 162°44'46″ = 0.30111365456 rad
∠ B' = β' = 98.62769265587° = 98°37'37″ = 1.4220228054 rad
∠ C' = γ' = 98.62769265587° = 98°37'37″ = 1.4220228054 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 = 6 ; ; b = 20 ; ; c = 20 ; ;

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

p = a+b+c = 6+20+20 = 46 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 46 }{ 2 } = 23 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23 * (23-6)(23-20)(23-20) } ; ; T = sqrt{ 3519 } = 59.32 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 59.32 }{ 6 } = 19.77 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 59.32 }{ 20 } = 5.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 59.32 }{ 20 } = 5.93 ; ;

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{ 6**2-20**2-20**2 }{ 2 * 20 * 20 } ) = 17° 15'14" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-6**2-20**2 }{ 2 * 6 * 20 } ) = 81° 22'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-6**2-20**2 }{ 2 * 20 * 6 } ) = 81° 22'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 59.32 }{ 23 } = 2.58 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 17° 15'14" } = 10.11 ; ;




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