10 16 20 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 16   c = 20

Area: T = 79.24401413426
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 29.68662952314° = 29°41'11″ = 0.51881235945 rad
Angle ∠ B = β = 52.41104970351° = 52°24'38″ = 0.91547357359 rad
Angle ∠ C = γ = 97.90332077335° = 97°54'12″ = 1.70987333232 rad

Height: ha = 15.84880282685
Height: hb = 9.90550176678
Height: hc = 7.92440141343

Median: ma = 17.40768951855
Median: mb = 13.6388181697
Median: mc = 8.83217608663

Inradius: r = 3.44552235366
Circumradius: R = 10.09658931477

Vertex coordinates: A[20; 0] B[0; 0] C[6.1; 7.92440141343]
Centroid: CG[8.7; 2.64113380448]
Coordinates of the circumscribed circle: U[10; -1.38881853078]
Coordinates of the inscribed circle: I[7; 3.44552235366]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.3143704769° = 150°18'49″ = 0.51881235945 rad
∠ B' = β' = 127.5989502965° = 127°35'22″ = 0.91547357359 rad
∠ C' = γ' = 82.09767922665° = 82°5'48″ = 1.70987333232 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 = 10 ; ; b = 16 ; ; c = 20 ; ;

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

p = a+b+c = 10+16+20 = 46 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 46 }{ 2 } = 23 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23 * (23-10)(23-16)(23-20) } ; ; T = sqrt{ 6279 } = 79.24 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 79.24 }{ 10 } = 15.85 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 79.24 }{ 16 } = 9.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 79.24 }{ 20 } = 7.92 ; ;

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{ 10**2-16**2-20**2 }{ 2 * 16 * 20 } ) = 29° 41'11" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-10**2-20**2 }{ 2 * 10 * 20 } ) = 52° 24'38" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-10**2-16**2 }{ 2 * 16 * 10 } ) = 97° 54'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 79.24 }{ 23 } = 3.45 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 29° 41'11" } = 10.1 ; ;




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