10 18 27 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 18   c = 27

Area: T = 47.81114787473
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 11.34772673825° = 11°20'50″ = 0.19880471769 rad
Angle ∠ B = β = 20.74219164807° = 20°44'31″ = 0.36220147358 rad
Angle ∠ C = γ = 147.9110816137° = 147°54'39″ = 2.58215307409 rad

Height: ha = 9.56222957495
Height: hb = 5.31223865275
Height: hc = 3.54215910183

Median: ma = 22.39441956766
Median: mb = 18.26219823677
Median: mc = 5.45443560573

Inradius: r = 1.73985992272
Circumradius: R = 25.41223075009

Vertex coordinates: A[27; 0] B[0; 0] C[9.35218518519; 3.54215910183]
Centroid: CG[12.11772839506; 1.18105303394]
Coordinates of the circumscribed circle: U[13.5; -21.53298716327]
Coordinates of the inscribed circle: I[9.5; 1.73985992272]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.6532732617° = 168°39'10″ = 0.19880471769 rad
∠ B' = β' = 159.2588083519° = 159°15'29″ = 0.36220147358 rad
∠ C' = γ' = 32.08991838633° = 32°5'21″ = 2.58215307409 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 = 10 ; ; b = 18 ; ; c = 27 ; ;

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

p = a+b+c = 10+18+27 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-10)(27.5-18)(27.5-27) } ; ; T = sqrt{ 2285.94 } = 47.81 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 47.81 }{ 10 } = 9.56 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 47.81 }{ 18 } = 5.31 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 47.81 }{ 27 } = 3.54 ; ;

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{ 10**2-18**2-27**2 }{ 2 * 18 * 27 } ) = 11° 20'50" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-10**2-27**2 }{ 2 * 10 * 27 } ) = 20° 44'31" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-10**2-18**2 }{ 2 * 18 * 10 } ) = 147° 54'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 47.81 }{ 27.5 } = 1.74 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 11° 20'50" } = 25.41 ; ;




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