4 16 18 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 16   c = 18

Area: T = 29.24403830344
Perimeter: p = 38
Semiperimeter: s = 19

Angle ∠ A = α = 11.71658523949° = 11°42'57″ = 0.2044480199 rad
Angle ∠ B = β = 54.31546652873° = 54°18'53″ = 0.94879697414 rad
Angle ∠ C = γ = 113.9699482318° = 113°58'10″ = 1.98991427132 rad

Height: ha = 14.62201915172
Height: hb = 3.65550478793
Height: hc = 3.24989314483

Median: ma = 16.91215345253
Median: mb = 10.2965630141
Median: mc = 7.41661984871

Inradius: r = 1.53989675281
Circumradius: R = 9.849939218

Vertex coordinates: A[18; 0] B[0; 0] C[2.33333333333; 3.24989314483]
Centroid: CG[6.77877777778; 1.08329771494]
Coordinates of the circumscribed circle: U[9; -4.00113155731]
Coordinates of the inscribed circle: I[3; 1.53989675281]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.2844147605° = 168°17'3″ = 0.2044480199 rad
∠ B' = β' = 125.6855334713° = 125°41'7″ = 0.94879697414 rad
∠ C' = γ' = 66.03105176822° = 66°1'50″ = 1.98991427132 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 = 4 ; ; b = 16 ; ; c = 18 ; ;

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

p = a+b+c = 4+16+18 = 38 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 38 }{ 2 } = 19 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19 * (19-4)(19-16)(19-18) } ; ; T = sqrt{ 855 } = 29.24 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 29.24 }{ 4 } = 14.62 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 29.24 }{ 16 } = 3.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 29.24 }{ 18 } = 3.25 ; ;

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{ 4**2-16**2-18**2 }{ 2 * 16 * 18 } ) = 11° 42'57" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-4**2-18**2 }{ 2 * 4 * 18 } ) = 54° 18'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-4**2-16**2 }{ 2 * 16 * 4 } ) = 113° 58'10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 29.24 }{ 19 } = 1.54 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 11° 42'57" } = 9.85 ; ;




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