8 16 22 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 16   c = 22

Area: T = 49.14326495012
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 16.2143633496° = 16°12'49″ = 0.28329812882 rad
Angle ∠ B = β = 33.9487926527° = 33°56'53″ = 0.59325030921 rad
Angle ∠ C = γ = 129.8388439977° = 129°50'18″ = 2.26661082733 rad

Height: ha = 12.28656623753
Height: hb = 6.14328311877
Height: hc = 4.4687513591

Median: ma = 18.81548877222
Median: mb = 14.49113767462
Median: mc = 6.24549979984

Inradius: r = 2.13766369348
Circumradius: R = 14.3265641925

Vertex coordinates: A[22; 0] B[0; 0] C[6.63663636364; 4.4687513591]
Centroid: CG[9.54554545455; 1.4899171197]
Coordinates of the circumscribed circle: U[11; -9.17773643582]
Coordinates of the inscribed circle: I[7; 2.13766369348]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.7866366504° = 163°47'11″ = 0.28329812882 rad
∠ B' = β' = 146.0522073473° = 146°3'7″ = 0.59325030921 rad
∠ C' = γ' = 50.1621560023° = 50°9'42″ = 2.26661082733 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 = 8 ; ; b = 16 ; ; c = 22 ; ;

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

p = a+b+c = 8+16+22 = 46 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 46 }{ 2 } = 23 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23 * (23-8)(23-16)(23-22) } ; ; T = sqrt{ 2415 } = 49.14 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 49.14 }{ 8 } = 12.29 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 49.14 }{ 16 } = 6.14 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 49.14 }{ 22 } = 4.47 ; ;

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{ 8**2-16**2-22**2 }{ 2 * 16 * 22 } ) = 16° 12'49" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-8**2-22**2 }{ 2 * 8 * 22 } ) = 33° 56'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-8**2-16**2 }{ 2 * 16 * 8 } ) = 129° 50'18" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 49.14 }{ 23 } = 2.14 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 16° 12'49" } = 14.33 ; ;




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