6 13 18 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 13   c = 18

Area: T = 25.21878012523
Perimeter: p = 37
Semiperimeter: s = 18.5

Angle ∠ A = α = 12.44770198968° = 12°26'49″ = 0.21772414793 rad
Angle ∠ B = β = 27.83994971122° = 27°50'22″ = 0.48658908867 rad
Angle ∠ C = γ = 139.7133482991° = 139°42'49″ = 2.43884602876 rad

Height: ha = 8.40659337508
Height: hb = 3.88796617311
Height: hc = 2.80219779169

Median: ma = 15.41110350074
Median: mb = 11.73766945943
Median: mc = 4.63768092477

Inradius: r = 1.3633124392
Circumradius: R = 13.91987392465

Vertex coordinates: A[18; 0] B[0; 0] C[5.30655555556; 2.80219779169]
Centroid: CG[7.76985185185; 0.9343992639]
Coordinates of the circumscribed circle: U[9; -10.61774998098]
Coordinates of the inscribed circle: I[5.5; 1.3633124392]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.5532980103° = 167°33'11″ = 0.21772414793 rad
∠ B' = β' = 152.1610502888° = 152°9'38″ = 0.48658908867 rad
∠ C' = γ' = 40.2876517009° = 40°17'11″ = 2.43884602876 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 = 6 ; ; b = 13 ; ; c = 18 ; ;

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

p = a+b+c = 6+13+18 = 37 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 37 }{ 2 } = 18.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18.5 * (18.5-6)(18.5-13)(18.5-18) } ; ; T = sqrt{ 635.94 } = 25.22 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 25.22 }{ 6 } = 8.41 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 25.22 }{ 13 } = 3.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 25.22 }{ 18 } = 2.8 ; ;

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{ 6**2-13**2-18**2 }{ 2 * 13 * 18 } ) = 12° 26'49" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-6**2-18**2 }{ 2 * 6 * 18 } ) = 27° 50'22" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-6**2-13**2 }{ 2 * 13 * 6 } ) = 139° 42'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 25.22 }{ 18.5 } = 1.36 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 12° 26'49" } = 13.92 ; ;




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