2 12 12 triangle

Acute isosceles triangle.

Sides: a = 2   b = 12   c = 12

Area: T = 11.95882607431
Perimeter: p = 26
Semiperimeter: s = 13

Angle ∠ A = α = 9.56603836944° = 9°33'37″ = 0.16768601732 rad
Angle ∠ B = β = 85.22198081528° = 85°13'11″ = 1.48773662402 rad
Angle ∠ C = γ = 85.22198081528° = 85°13'11″ = 1.48773662402 rad

Height: ha = 11.95882607431
Height: hb = 1.99330434572
Height: hc = 1.99330434572

Median: ma = 11.95882607431
Median: mb = 6.1644414003
Median: mc = 6.1644414003

Inradius: r = 0.9219866211
Circumradius: R = 6.02109424721

Vertex coordinates: A[12; 0] B[0; 0] C[0.16766666667; 1.99330434572]
Centroid: CG[4.05655555556; 0.66443478191]
Coordinates of the circumscribed circle: U[6; 0.5021745206]
Coordinates of the inscribed circle: I[1; 0.9219866211]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.4439616306° = 170°26'23″ = 0.16768601732 rad
∠ B' = β' = 94.78801918472° = 94°46'49″ = 1.48773662402 rad
∠ C' = γ' = 94.78801918472° = 94°46'49″ = 1.48773662402 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 = 2 ; ; b = 12 ; ; c = 12 ; ;

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

p = a+b+c = 2+12+12 = 26 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 26 }{ 2 } = 13 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13 * (13-2)(13-12)(13-12) } ; ; T = sqrt{ 143 } = 11.96 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 11.96 }{ 2 } = 11.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 11.96 }{ 12 } = 1.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 11.96 }{ 12 } = 1.99 ; ;

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{ 2**2-12**2-12**2 }{ 2 * 12 * 12 } ) = 9° 33'37" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-2**2-12**2 }{ 2 * 2 * 12 } ) = 85° 13'11" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 12**2-2**2-12**2 }{ 2 * 12 * 2 } ) = 85° 13'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 11.96 }{ 13 } = 0.92 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 9° 33'37" } = 6.02 ; ;




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