6 16 21 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 16   c = 21

Area: T = 30.27327187415
Perimeter: p = 43
Semiperimeter: s = 21.5

Angle ∠ A = α = 10.38111039012° = 10°22'52″ = 0.18111844431 rad
Angle ∠ B = β = 28.71993267538° = 28°43'10″ = 0.50112468108 rad
Angle ∠ C = γ = 140.9899569345° = 140°53'58″ = 2.45991613997 rad

Height: ha = 10.09109062472
Height: hb = 3.78440898427
Height: hc = 2.88331160706

Median: ma = 18.42655257727
Median: mb = 13.21098448136
Median: mc = 5.97991303716

Inradius: r = 1.40880334298
Circumradius: R = 16.64986533405

Vertex coordinates: A[21; 0] B[0; 0] C[5.26219047619; 2.88331160706]
Centroid: CG[8.7543968254; 0.96110386902]
Coordinates of the circumscribed circle: U[10.5; -12.92200486861]
Coordinates of the inscribed circle: I[5.5; 1.40880334298]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.6198896099° = 169°37'8″ = 0.18111844431 rad
∠ B' = β' = 151.2810673246° = 151°16'50″ = 0.50112468108 rad
∠ C' = γ' = 39.11004306549° = 39°6'2″ = 2.45991613997 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 = 21 ; ;

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

p = a+b+c = 6+16+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 * (21.5-6)(21.5-16)(21.5-21) } ; ; T = sqrt{ 916.44 } = 30.27 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 30.27 }{ 6 } = 10.09 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 30.27 }{ 16 } = 3.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 30.27 }{ 21 } = 2.88 ; ;

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**2-21**2 }{ 2 * 16 * 21 } ) = 10° 22'52" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-6**2-21**2 }{ 2 * 6 * 21 } ) = 28° 43'10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 21**2-6**2-16**2 }{ 2 * 16 * 6 } ) = 140° 53'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 30.27 }{ 21.5 } = 1.41 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 10° 22'52" } = 16.65 ; ;




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