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: h_a = 10.79106209275
Height: h_b = 1.79884368212
Height: h_c = 1.66600955273

Median: m_a = 12.47699639133
Median: m_b = 7.10663352018
Median: m_c = 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

Calculate another triangle

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

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

6. Inradius

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

7. Circumradius

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

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