3 12 14 triangle

Obtuse scalene triangle.

Sides: a = 3   b = 12   c = 14

Area: T = 14.4377364718
Perimeter: p = 29
Semiperimeter: s = 14.5

Angle ∠ A = α = 9.89767597741° = 9°53'48″ = 0.17327310433 rad
Angle ∠ B = β = 43.43220282875° = 43°25'55″ = 0.75880318944 rad
Angle ∠ C = γ = 126.6711211938° = 126°40'16″ = 2.21108297158 rad

Height: ha = 9.6254909812
Height: hb = 2.4066227453
Height: hc = 2.0622480674

Median: ma = 12.9521833847
Median: mb = 8.15547532152
Median: mc = 5.24440442409

Inradius: r = 0.99656803254
Circumradius: R = 8.72773545042

Vertex coordinates: A[14; 0] B[0; 0] C[2.17985714286; 2.0622480674]
Centroid: CG[5.39328571429; 0.6877493558]
Coordinates of the circumscribed circle: U[7; -5.21221700511]
Coordinates of the inscribed circle: I[2.5; 0.99656803254]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.1033240226° = 170°6'12″ = 0.17327310433 rad
∠ B' = β' = 136.5687971712° = 136°34'5″ = 0.75880318944 rad
∠ C' = γ' = 53.32987880616° = 53°19'44″ = 2.21108297158 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 = 3 ; ; b = 12 ; ; c = 14 ; ;

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

p = a+b+c = 3+12+14 = 29 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 29 }{ 2 } = 14.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 14.5 * (14.5-3)(14.5-12)(14.5-14) } ; ; T = sqrt{ 208.44 } = 14.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 14.44 }{ 3 } = 9.62 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 14.44 }{ 12 } = 2.41 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 14.44 }{ 14 } = 2.06 ; ;

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{ 3**2-12**2-14**2 }{ 2 * 12 * 14 } ) = 9° 53'48" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-3**2-14**2 }{ 2 * 3 * 14 } ) = 43° 25'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14**2-3**2-12**2 }{ 2 * 12 * 3 } ) = 126° 40'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 14.44 }{ 14.5 } = 1 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 9° 53'48" } = 8.73 ; ;




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