1 12 12 triangle

Acute isosceles triangle.

Sides: a = 1   b = 12   c = 12

Area: T = 5.99547894041
Perimeter: p = 25
Semiperimeter: s = 12.5

Angle ∠ A = α = 4.77660309265° = 4°46'34″ = 0.08333574648 rad
Angle ∠ B = β = 87.61219845367° = 87°36'43″ = 1.52991175944 rad
Angle ∠ C = γ = 87.61219845367° = 87°36'43″ = 1.52991175944 rad

Height: ha = 11.99895788083
Height: hb = 0.99991315674
Height: hc = 0.99991315674

Median: ma = 11.99895788083
Median: mb = 6.04215229868
Median: mc = 6.04215229868

Inradius: r = 0.48795831523
Circumradius: R = 6.00552151248

Vertex coordinates: A[12; 0] B[0; 0] C[0.04216666667; 0.99991315674]
Centroid: CG[4.01438888889; 0.33330438558]
Coordinates of the circumscribed circle: U[6; 0.25502172969]
Coordinates of the inscribed circle: I[0.5; 0.48795831523]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 175.2243969073° = 175°13'26″ = 0.08333574648 rad
∠ B' = β' = 92.38880154633° = 92°23'17″ = 1.52991175944 rad
∠ C' = γ' = 92.38880154633° = 92°23'17″ = 1.52991175944 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 = 12 ; ; c = 12 ; ;

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

p = a+b+c = 1+12+12 = 25 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 25 }{ 2 } = 12.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12.5 * (12.5-1)(12.5-12)(12.5-12) } ; ; T = sqrt{ 35.94 } = 5.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5.99 }{ 1 } = 11.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5.99 }{ 12 } = 1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5.99 }{ 12 } = 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**2-12**2-12**2 }{ 2 * 12 * 12 } ) = 4° 46'34" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-1**2-12**2 }{ 2 * 1 * 12 } ) = 87° 36'43" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 12**2-1**2-12**2 }{ 2 * 12 * 1 } ) = 87° 36'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5.99 }{ 12.5 } = 0.48 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1 }{ 2 * sin 4° 46'34" } = 6.01 ; ;




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