9 16 22 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 16   c = 22

Area: T = 61.91547599527
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 20.59767412641° = 20°35'48″ = 0.35994809502 rad
Angle ∠ B = β = 38.71216710509° = 38°42'42″ = 0.67656461188 rad
Angle ∠ C = γ = 120.6921587685° = 120°41'30″ = 2.10664655846 rad

Height: ha = 13.7598835545
Height: hb = 7.73993449941
Height: hc = 5.62986145412

Median: ma = 18.70216042093
Median: mb = 14.78217454991
Median: mc = 6.8922024376

Inradius: r = 2.63546706363
Circumradius: R = 12.79217801927

Vertex coordinates: A[22; 0] B[0; 0] C[7.02327272727; 5.62986145412]
Centroid: CG[9.67442424242; 1.87662048471]
Coordinates of the circumscribed circle: U[11; -6.52991378067]
Coordinates of the inscribed circle: I[7.5; 2.63546706363]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.4033258736° = 159°24'12″ = 0.35994809502 rad
∠ B' = β' = 141.2888328949° = 141°17'18″ = 0.67656461188 rad
∠ C' = γ' = 59.30884123151° = 59°18'30″ = 2.10664655846 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 = 9 ; ; b = 16 ; ; c = 22 ; ;

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

p = a+b+c = 9+16+22 = 47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 47 }{ 2 } = 23.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23.5 * (23.5-9)(23.5-16)(23.5-22) } ; ; T = sqrt{ 3833.44 } = 61.91 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 61.91 }{ 9 } = 13.76 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 61.91 }{ 16 } = 7.74 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 61.91 }{ 22 } = 5.63 ; ;

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{ 9**2-16**2-22**2 }{ 2 * 16 * 22 } ) = 20° 35'48" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-9**2-22**2 }{ 2 * 9 * 22 } ) = 38° 42'42" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-9**2-16**2 }{ 2 * 16 * 9 } ) = 120° 41'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 61.91 }{ 23.5 } = 2.63 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 20° 35'48" } = 12.79 ; ;




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