16 16 23 triangle

Obtuse isosceles triangle.

Sides: a = 16   b = 16   c = 23

Area: T = 127.9299423902
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 44.04986256741° = 44°2'55″ = 0.7698793549 rad
Angle ∠ B = β = 44.04986256741° = 44°2'55″ = 0.7698793549 rad
Angle ∠ C = γ = 91.90327486518° = 91°54'10″ = 1.60440055556 rad

Height: ha = 15.99111779878
Height: hb = 15.99111779878
Height: hc = 11.12442977306

Median: ma = 18.12545689604
Median: mb = 18.12545689604
Median: mc = 11.12442977306

Inradius: r = 4.6521979051
Circumradius: R = 11.50663443194

Vertex coordinates: A[23; 0] B[0; 0] C[11.5; 11.12442977306]
Centroid: CG[11.5; 3.70880992435]
Coordinates of the circumscribed circle: U[11.5; -0.38220465887]
Coordinates of the inscribed circle: I[11.5; 4.6521979051]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.9511374326° = 135°57'5″ = 0.7698793549 rad
∠ B' = β' = 135.9511374326° = 135°57'5″ = 0.7698793549 rad
∠ C' = γ' = 88.09772513482° = 88°5'50″ = 1.60440055556 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 = 23 ; ;

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

p = a+b+c = 16+16+23 = 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 * (27.5-16)(27.5-16)(27.5-23) } ; ; T = sqrt{ 16365.94 } = 127.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 127.93 }{ 16 } = 15.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 127.93 }{ 16 } = 15.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 127.93 }{ 23 } = 11.12 ; ;

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**2-23**2 }{ 2 * 16 * 23 } ) = 44° 2'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-16**2-23**2 }{ 2 * 16 * 23 } ) = 44° 2'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-16**2-16**2 }{ 2 * 16 * 16 } ) = 91° 54'10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 127.93 }{ 27.5 } = 4.65 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 44° 2'55" } = 11.51 ; ;




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