2 11 12 triangle

Obtuse scalene triangle.

Sides: a = 2   b = 11   c = 12

Area: T = 9.92215674165
Perimeter: p = 25
Semiperimeter: s = 12.5

Angle ∠ A = α = 8.64658643504° = 8°38'45″ = 0.15108987996 rad
Angle ∠ B = β = 55.77111336722° = 55°46'16″ = 0.97333899101 rad
Angle ∠ C = γ = 115.5833001977° = 115°34'59″ = 2.01773039438 rad

Height: ha = 9.92215674165
Height: hb = 1.80439213485
Height: hc = 1.65435945694

Median: ma = 11.46773449412
Median: mb = 6.61443782777
Median: mc = 5.14878150705

Inradius: r = 0.79437253933
Circumradius: R = 6.6522174725

Vertex coordinates: A[12; 0] B[0; 0] C[1.125; 1.65435945694]
Centroid: CG[4.375; 0.55111981898]
Coordinates of the circumscribed circle: U[6; -2.87325299949]
Coordinates of the inscribed circle: I[1.5; 0.79437253933]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 171.354413565° = 171°21'15″ = 0.15108987996 rad
∠ B' = β' = 124.2298866328° = 124°13'44″ = 0.97333899101 rad
∠ C' = γ' = 64.41769980226° = 64°25'1″ = 2.01773039438 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 = 11 ; ; c = 12 ; ;

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

p = a+b+c = 2+11+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 * (12.5-2)(12.5-11)(12.5-12) } ; ; T = sqrt{ 98.44 } = 9.92 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 9.92 }{ 2 } = 9.92 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 9.92 }{ 11 } = 1.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 9.92 }{ 12 } = 1.65 ; ;

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**2-11**2-12**2 }{ 2 * 11 * 12 } ) = 8° 38'45" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-2**2-12**2 }{ 2 * 2 * 12 } ) = 55° 46'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 12**2-2**2-11**2 }{ 2 * 11 * 2 } ) = 115° 34'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 9.92 }{ 12.5 } = 0.79 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 8° 38'45" } = 6.65 ; ;




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