16 18 27 triangle

Obtuse scalene triangle.

Sides: a = 16   b = 18   c = 27

Area: T = 139.0998661029
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 34.91993255344° = 34°55'10″ = 0.60994572032 rad
Angle ∠ B = β = 40.08988890862° = 40°5'20″ = 0.7699683108 rad
Angle ∠ C = γ = 104.9921785379° = 104°59'30″ = 1.83224523424 rad

Height: ha = 17.38773326286
Height: hb = 15.4555406781
Height: hc = 10.30436045207

Median: ma = 21.50658131676
Median: mb = 20.28554627751
Median: mc = 10.3880269746

Inradius: r = 4.5610611837
Circumradius: R = 13.97656916826

Vertex coordinates: A[27; 0] B[0; 0] C[12.24107407407; 10.30436045207]
Centroid: CG[13.08802469136; 3.43545348402]
Coordinates of the circumscribed circle: U[13.5; -3.61552396887]
Coordinates of the inscribed circle: I[12.5; 4.5610611837]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.0810674466° = 145°4'50″ = 0.60994572032 rad
∠ B' = β' = 139.9111110914° = 139°54'40″ = 0.7699683108 rad
∠ C' = γ' = 75.00882146206° = 75°30″ = 1.83224523424 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 = 16 ; ; b = 18 ; ; c = 27 ; ;

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

p = a+b+c = 16+18+27 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-16)(30.5-18)(30.5-27) } ; ; T = sqrt{ 19348.44 } = 139.1 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 139.1 }{ 16 } = 17.39 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 139.1 }{ 18 } = 15.46 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 139.1 }{ 27 } = 10.3 ; ;

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{ 16**2-18**2-27**2 }{ 2 * 18 * 27 } ) = 34° 55'10" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-16**2-27**2 }{ 2 * 16 * 27 } ) = 40° 5'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-16**2-18**2 }{ 2 * 18 * 16 } ) = 104° 59'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 139.1 }{ 30.5 } = 4.56 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 34° 55'10" } = 13.98 ; ;




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