2 13 14 triangle

Obtuse scalene triangle.

Sides: a = 2   b = 13   c = 14

Area: T = 11.65992238164
Perimeter: p = 29
Semiperimeter: s = 14.5

Angle ∠ A = α = 7.36111606635° = 7°21'40″ = 0.12884764903 rad
Angle ∠ B = β = 56.38876254015° = 56°23'15″ = 0.98441497206 rad
Angle ∠ C = γ = 116.2511213935° = 116°15'4″ = 2.02989664426 rad

Height: ha = 11.65992238164
Height: hb = 1.7943726741
Height: hc = 1.66656034023

Median: ma = 13.47221935853
Median: mb = 7.59993420768
Median: mc = 6.1243724357

Inradius: r = 0.80440844011
Circumradius: R = 7.80549792536

Vertex coordinates: A[14; 0] B[0; 0] C[1.10771428571; 1.66656034023]
Centroid: CG[5.03657142857; 0.55552011341]
Coordinates of the circumscribed circle: U[7; -3.45222023622]
Coordinates of the inscribed circle: I[1.5; 0.80440844011]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 172.6398839336° = 172°38'20″ = 0.12884764903 rad
∠ B' = β' = 123.6122374598° = 123°36'45″ = 0.98441497206 rad
∠ C' = γ' = 63.7498786065° = 63°44'56″ = 2.02989664426 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 = 13 ; ; c = 14 ; ;

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

p = a+b+c = 2+13+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 * (14.5-2)(14.5-13)(14.5-14) } ; ; T = sqrt{ 135.94 } = 11.66 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 11.66 }{ 2 } = 11.66 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 11.66 }{ 13 } = 1.79 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 11.66 }{ 14 } = 1.67 ; ;

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**2-13**2-14**2 }{ 2 * 13 * 14 } ) = 7° 21'40" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-2**2-14**2 }{ 2 * 2 * 14 } ) = 56° 23'15" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14**2-2**2-13**2 }{ 2 * 13 * 2 } ) = 116° 15'4" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 11.66 }{ 14.5 } = 0.8 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 7° 21'40" } = 7.8 ; ;




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