5 16 20 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 16   c = 20

Area: T = 26.7388315205
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 9.62200904201° = 9°37'12″ = 0.16879022522 rad
Angle ∠ B = β = 32.32880641222° = 32°19'41″ = 0.56442311597 rad
Angle ∠ C = γ = 138.0521845458° = 138°3'7″ = 2.40994592417 rad

Height: ha = 10.6955326082
Height: hb = 3.34222894006
Height: hc = 2.67438315205

Median: ma = 17.93773911147
Median: mb = 12.1866057607
Median: mc = 6.36439610307

Inradius: r = 1.30443080588
Circumradius: R = 14.96598056921

Vertex coordinates: A[20; 0] B[0; 0] C[4.225; 2.67438315205]
Centroid: CG[8.075; 0.89112771735]
Coordinates of the circumscribed circle: U[10; -11.12663554835]
Coordinates of the inscribed circle: I[4.5; 1.30443080588]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.387990958° = 170°22'48″ = 0.16879022522 rad
∠ B' = β' = 147.6721935878° = 147°40'19″ = 0.56442311597 rad
∠ C' = γ' = 41.94881545423° = 41°56'53″ = 2.40994592417 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 = 5 ; ; b = 16 ; ; c = 20 ; ;

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

p = a+b+c = 5+16+20 = 41 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 41 }{ 2 } = 20.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.5 * (20.5-5)(20.5-16)(20.5-20) } ; ; T = sqrt{ 714.94 } = 26.74 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 26.74 }{ 5 } = 10.7 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 26.74 }{ 16 } = 3.34 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 26.74 }{ 20 } = 2.67 ; ;

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{ 5**2-16**2-20**2 }{ 2 * 16 * 20 } ) = 9° 37'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-5**2-20**2 }{ 2 * 5 * 20 } ) = 32° 19'41" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-5**2-16**2 }{ 2 * 16 * 5 } ) = 138° 3'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 26.74 }{ 20.5 } = 1.3 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 9° 37'12" } = 14.96 ; ;




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