12 12 20 triangle

Obtuse isosceles triangle.

Sides: a = 12   b = 12   c = 20

Area: T = 66.33224958071
Perimeter: p = 44
Semiperimeter: s = 22

Angle ∠ A = α = 33.55773097619° = 33°33'26″ = 0.58656855435 rad
Angle ∠ B = β = 33.55773097619° = 33°33'26″ = 0.58656855435 rad
Angle ∠ C = γ = 112.8855380476° = 112°53'7″ = 1.97702215667 rad

Height: ha = 11.05554159679
Height: hb = 11.05554159679
Height: hc = 6.63332495807

Median: ma = 15.36222914957
Median: mb = 15.36222914957
Median: mc = 6.63332495807

Inradius: r = 3.01551134458
Circumradius: R = 10.85444084048

Vertex coordinates: A[20; 0] B[0; 0] C[10; 6.63332495807]
Centroid: CG[10; 2.21110831936]
Coordinates of the circumscribed circle: U[10; -4.22111588241]
Coordinates of the inscribed circle: I[10; 3.01551134458]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.4432690238° = 146°26'34″ = 0.58656855435 rad
∠ B' = β' = 146.4432690238° = 146°26'34″ = 0.58656855435 rad
∠ C' = γ' = 67.11546195238° = 67°6'53″ = 1.97702215667 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 = 12 ; ; b = 12 ; ; c = 20 ; ;

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

p = a+b+c = 12+12+20 = 44 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 44 }{ 2 } = 22 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22 * (22-12)(22-12)(22-20) } ; ; T = sqrt{ 4400 } = 66.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 66.33 }{ 12 } = 11.06 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 66.33 }{ 12 } = 11.06 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 66.33 }{ 20 } = 6.63 ; ;

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{ 12**2-12**2-20**2 }{ 2 * 12 * 20 } ) = 33° 33'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-12**2-20**2 }{ 2 * 12 * 20 } ) = 33° 33'26" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-12**2-12**2 }{ 2 * 12 * 12 } ) = 112° 53'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 66.33 }{ 22 } = 3.02 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 33° 33'26" } = 10.85 ; ;




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