6 16 20 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 16   c = 20

Area: T = 39.6866269666
Perimeter: p = 42
Semiperimeter: s = 21

Angle ∠ A = α = 14.36215115629° = 14°21'41″ = 0.25106556623 rad
Angle ∠ B = β = 41.41096221093° = 41°24'35″ = 0.72327342478 rad
Angle ∠ C = γ = 124.2298866328° = 124°13'44″ = 2.16882027434 rad

Height: ha = 13.22987565553
Height: hb = 4.96107837082
Height: hc = 3.96986269666

Median: ma = 17.86105710995
Median: mb = 12.4109673646
Median: mc = 6.78223299831

Inradius: r = 1.8989822365
Circumradius: R = 12.09548631363

Vertex coordinates: A[20; 0] B[0; 0] C[4.5; 3.96986269666]
Centroid: CG[8.16766666667; 1.32328756555]
Coordinates of the circumscribed circle: U[10; -6.80333605142]
Coordinates of the inscribed circle: I[5; 1.8989822365]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.6388488437° = 165°38'19″ = 0.25106556623 rad
∠ B' = β' = 138.5990377891° = 138°35'25″ = 0.72327342478 rad
∠ C' = γ' = 55.77111336722° = 55°46'16″ = 2.16882027434 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 = 6 ; ; b = 16 ; ; c = 20 ; ;

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

p = a+b+c = 6+16+20 = 42 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 42 }{ 2 } = 21 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21 * (21-6)(21-16)(21-20) } ; ; T = sqrt{ 1575 } = 39.69 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 39.69 }{ 6 } = 13.23 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 39.69 }{ 16 } = 4.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 39.69 }{ 20 } = 3.97 ; ;

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{ 6**2-16**2-20**2 }{ 2 * 16 * 20 } ) = 14° 21'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-6**2-20**2 }{ 2 * 6 * 20 } ) = 41° 24'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-6**2-16**2 }{ 2 * 16 * 6 } ) = 124° 13'44" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 39.69 }{ 21 } = 1.89 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 14° 21'41" } = 12.09 ; ;




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