2 12 13 triangle

Obtuse scalene triangle.

Sides: a = 2   b = 12   c = 13

Area: T = 10.79106209275
Perimeter: p = 27
Semiperimeter: s = 13.5

Angle ∠ A = α = 7.95218754307° = 7°57'7″ = 0.1398786408 rad
Angle ∠ B = β = 56.1043644797° = 56°6'13″ = 0.97991933241 rad
Angle ∠ C = γ = 115.9444479772° = 115°56'40″ = 2.02436129215 rad

Height: ha = 10.79106209275
Height: hb = 1.79884368212
Height: hc = 1.66600955273

Median: ma = 12.47699639133
Median: mb = 7.10663352018
Median: mc = 5.63547138348

Inradius: r = 0.79993052539
Circumradius: R = 7.22884996873

Vertex coordinates: A[13; 0] B[0; 0] C[1.11553846154; 1.66600955273]
Centroid: CG[4.70551282051; 0.55333651758]
Coordinates of the circumscribed circle: U[6.5; -3.16224686132]
Coordinates of the inscribed circle: I[1.5; 0.79993052539]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 172.0488124569° = 172°2'53″ = 0.1398786408 rad
∠ B' = β' = 123.8966355203° = 123°53'47″ = 0.97991933241 rad
∠ C' = γ' = 64.05655202276° = 64°3'20″ = 2.02436129215 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 = 13 ; ;

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

p = a+b+c = 2+12+13 = 27 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 27 }{ 2 } = 13.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13.5 * (13.5-2)(13.5-12)(13.5-13) } ; ; T = sqrt{ 116.44 } = 10.79 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 10.79 }{ 2 } = 10.79 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 10.79 }{ 12 } = 1.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 10.79 }{ 13 } = 1.66 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 12**2+13**2-2**2 }{ 2 * 12 * 13 } ) = 7° 57'7" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 2**2+13**2-12**2 }{ 2 * 2 * 13 } ) = 56° 6'13" ; ; gamma = 180° - alpha - beta = 180° - 7° 57'7" - 56° 6'13" = 115° 56'40" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 10.79 }{ 13.5 } = 0.8 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 2 }{ 2 * sin 7° 57'7" } = 7.23 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 12**2+2 * 13**2 - 2**2 } }{ 2 } = 12.47 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 13**2+2 * 2**2 - 12**2 } }{ 2 } = 7.106 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 12**2+2 * 2**2 - 13**2 } }{ 2 } = 5.635 ; ;
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