20 20 27 triangle

Acute isosceles triangle.

Sides: a = 20   b = 20   c = 27

Area: T = 199.2110786606
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 47.54658497956° = 47°32'45″ = 0.83298316246 rad
Angle ∠ B = β = 47.54658497956° = 47°32'45″ = 0.83298316246 rad
Angle ∠ C = γ = 84.90883004088° = 84°54'30″ = 1.48219294044 rad

Height: ha = 19.92110786606
Height: hb = 19.92110786606
Height: hc = 14.75663545634

Median: ma = 21.55222620623
Median: mb = 21.55222620623
Median: mc = 14.75663545634

Inradius: r = 5.94765906449
Circumradius: R = 13.55334829514

Vertex coordinates: A[27; 0] B[0; 0] C[13.5; 14.75663545634]
Centroid: CG[13.5; 4.91987848545]
Coordinates of the circumscribed circle: U[13.5; 1.20328716119]
Coordinates of the inscribed circle: I[13.5; 5.94765906449]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.4544150204° = 132°27'15″ = 0.83298316246 rad
∠ B' = β' = 132.4544150204° = 132°27'15″ = 0.83298316246 rad
∠ C' = γ' = 95.09216995912° = 95°5'30″ = 1.48219294044 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 = 20 ; ; b = 20 ; ; c = 27 ; ;

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

p = a+b+c = 20+20+27 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-20)(33.5-20)(33.5-27) } ; ; T = sqrt{ 39684.94 } = 199.21 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 199.21 }{ 20 } = 19.92 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 199.21 }{ 20 } = 19.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 199.21 }{ 27 } = 14.76 ; ;

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{ 20**2-20**2-27**2 }{ 2 * 20 * 27 } ) = 47° 32'45" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-20**2-27**2 }{ 2 * 20 * 27 } ) = 47° 32'45" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-20**2-20**2 }{ 2 * 20 * 20 } ) = 84° 54'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 199.21 }{ 33.5 } = 5.95 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 20 }{ 2 * sin 47° 32'45" } = 13.55 ; ;




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