2 20 21 triangle

Obtuse scalene triangle.

Sides: a = 2   b = 20   c = 21

Area: T = 17.73223856263
Perimeter: p = 43
Semiperimeter: s = 21.5

Angle ∠ A = α = 4.84438195264° = 4°50'38″ = 0.08545405991 rad
Angle ∠ B = β = 57.60876345142° = 57°36'27″ = 1.00554428966 rad
Angle ∠ C = γ = 117.5498545959° = 117°32'55″ = 2.05216091579 rad

Height: ha = 17.73223856263
Height: hb = 1.77332385626
Height: hc = 1.68987986311

Median: ma = 20.48216991483
Median: mb = 11.06879718106
Median: mc = 9.57986220303

Inradius: r = 0.82547621222
Circumradius: R = 11.84327381643

Vertex coordinates: A[21; 0] B[0; 0] C[1.07114285714; 1.68987986311]
Centroid: CG[7.35771428571; 0.5632932877]
Coordinates of the circumscribed circle: U[10.5; -5.4777266401]
Coordinates of the inscribed circle: I[1.5; 0.82547621222]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 175.1566180474° = 175°9'22″ = 0.08545405991 rad
∠ B' = β' = 122.3922365486° = 122°23'33″ = 1.00554428966 rad
∠ C' = γ' = 62.45114540405° = 62°27'5″ = 2.05216091579 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 = 2 ; ; b = 20 ; ; c = 21 ; ;

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

p = a+b+c = 2+20+21 = 43 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 43 }{ 2 } = 21.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21.5 * (21.5-2)(21.5-20)(21.5-21) } ; ; T = sqrt{ 314.44 } = 17.73 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 17.73 }{ 2 } = 17.73 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 17.73 }{ 20 } = 1.77 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 17.73 }{ 21 } = 1.69 ; ;

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{ 2**2-20**2-21**2 }{ 2 * 20 * 21 } ) = 4° 50'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-2**2-21**2 }{ 2 * 2 * 21 } ) = 57° 36'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 21**2-2**2-20**2 }{ 2 * 20 * 2 } ) = 117° 32'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 17.73 }{ 21.5 } = 0.82 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 4° 50'38" } = 11.84 ; ;




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