6 17 21 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 17   c = 21

Area: T = 41.95223539268
Perimeter: p = 44
Semiperimeter: s = 22

Angle ∠ A = α = 13.59332257052° = 13°35'36″ = 0.23772465445 rad
Angle ∠ B = β = 41.7522205202° = 41°45'8″ = 0.72987134507 rad
Angle ∠ C = γ = 124.6554569093° = 124°39'16″ = 2.17656326583 rad

Height: ha = 13.98441179756
Height: hb = 4.93655710502
Height: hc = 3.99554622787

Median: ma = 18.86879622641
Median: mb = 12.89437969582
Median: mc = 7.22884161474

Inradius: r = 1.90769251785
Circumradius: R = 12.76444804135

Vertex coordinates: A[21; 0] B[0; 0] C[4.47661904762; 3.99554622787]
Centroid: CG[8.49220634921; 1.33218207596]
Coordinates of the circumscribed circle: U[10.5; -7.25882339606]
Coordinates of the inscribed circle: I[5; 1.90769251785]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.4076774295° = 166°24'24″ = 0.23772465445 rad
∠ B' = β' = 138.2487794798° = 138°14'52″ = 0.72987134507 rad
∠ C' = γ' = 55.34554309073° = 55°20'44″ = 2.17656326583 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 = 17 ; ; c = 21 ; ;

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

p = a+b+c = 6+17+21 = 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 * (22-6)(22-17)(22-21) } ; ; T = sqrt{ 1760 } = 41.95 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 41.95 }{ 6 } = 13.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 41.95 }{ 17 } = 4.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 41.95 }{ 21 } = 4 ; ;

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**2-17**2-21**2 }{ 2 * 17 * 21 } ) = 13° 35'36" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-6**2-21**2 }{ 2 * 6 * 21 } ) = 41° 45'8" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 21**2-6**2-17**2 }{ 2 * 17 * 6 } ) = 124° 39'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 41.95 }{ 22 } = 1.91 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 13° 35'36" } = 12.76 ; ;




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