16 16 27 triangle

Obtuse isosceles triangle.

Sides: a = 16   b = 16   c = 27

Area: T = 115.9355057252
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 32.46217449672° = 32°27'42″ = 0.56765643306 rad
Angle ∠ B = β = 32.46217449672° = 32°27'42″ = 0.56765643306 rad
Angle ∠ C = γ = 115.0776510066° = 115°4'35″ = 2.00884639923 rad

Height: ha = 14.49218821565
Height: hb = 14.49218821565
Height: hc = 8.58877820187

Median: ma = 20.77002415445
Median: mb = 20.77002415445
Median: mc = 8.58877820187

Inradius: r = 3.93300019407
Circumradius: R = 14.90548962493

Vertex coordinates: A[27; 0] B[0; 0] C[13.5; 8.58877820187]
Centroid: CG[13.5; 2.86325940062]
Coordinates of the circumscribed circle: U[13.5; -6.31771142307]
Coordinates of the inscribed circle: I[13.5; 3.93300019407]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.5388255033° = 147°32'18″ = 0.56765643306 rad
∠ B' = β' = 147.5388255033° = 147°32'18″ = 0.56765643306 rad
∠ C' = γ' = 64.92334899345° = 64°55'25″ = 2.00884639923 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 = 16 ; ; c = 27 ; ;

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

p = a+b+c = 16+16+27 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-16)(29.5-16)(29.5-27) } ; ; T = sqrt{ 13440.94 } = 115.94 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 115.94 }{ 16 } = 14.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 115.94 }{ 16 } = 14.49 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 115.94 }{ 27 } = 8.59 ; ;

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**2-16**2-27**2 }{ 2 * 16 * 27 } ) = 32° 27'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-16**2-27**2 }{ 2 * 16 * 27 } ) = 32° 27'42" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-16**2-16**2 }{ 2 * 16 * 16 } ) = 115° 4'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 115.94 }{ 29.5 } = 3.93 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 32° 27'42" } = 14.9 ; ;




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