10 14 20 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 14   c = 20

Area: T = 64.99223072371
Perimeter: p = 44
Semiperimeter: s = 22

Angle ∠ A = α = 27.66604498993° = 27°39'38″ = 0.48327659233 rad
Angle ∠ B = β = 40.53658021113° = 40°32'9″ = 0.70774832118 rad
Angle ∠ C = γ = 111.8043747989° = 111°48'13″ = 1.95113435185 rad

Height: ha = 12.99884614474
Height: hb = 9.28546153196
Height: hc = 6.49992307237

Median: ma = 16.52327116419
Median: mb = 14.17774468788
Median: mc = 6.92882032303

Inradius: r = 2.95441957835
Circumradius: R = 10.77105054607

Vertex coordinates: A[20; 0] B[0; 0] C[7.6; 6.49992307237]
Centroid: CG[9.2; 2.16664102412]
Coordinates of the circumscribed circle: U[10; -44.0004734568]
Coordinates of the inscribed circle: I[8; 2.95441957835]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.3439550101° = 152°20'22″ = 0.48327659233 rad
∠ B' = β' = 139.4644197889° = 139°27'51″ = 0.70774832118 rad
∠ C' = γ' = 68.19662520106° = 68°11'47″ = 1.95113435185 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 = 14 ; ; c = 20 ; ;

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

p = a+b+c = 10+14+20 = 44 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 44 }{ 2 } = 22 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22 * (22-10)(22-14)(22-20) } ; ; T = sqrt{ 4224 } = 64.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 64.99 }{ 10 } = 13 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 64.99 }{ 14 } = 9.28 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 64.99 }{ 20 } = 6.5 ; ;

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**2-14**2-20**2 }{ 2 * 14 * 20 } ) = 27° 39'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-10**2-20**2 }{ 2 * 10 * 20 } ) = 40° 32'9" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-10**2-14**2 }{ 2 * 14 * 10 } ) = 111° 48'13" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 64.99 }{ 22 } = 2.95 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 27° 39'38" } = 10.77 ; ;




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