16 17 22 triangle

Acute scalene triangle.

Sides: a = 16   b = 17   c = 22

Area: T = 135.1422286128
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 46.27766909947° = 46°16'36″ = 0.80876806248 rad
Angle ∠ B = β = 50.1621560023° = 50°9'42″ = 0.87554843803 rad
Angle ∠ C = γ = 83.56217489823° = 83°33'42″ = 1.45884276485 rad

Height: ha = 16.8932785766
Height: hb = 15.89990924857
Height: hc = 12.28656623753

Median: ma = 17.95882849961
Median: mb = 17.25554339267
Median: mc = 12.30985336251

Inradius: r = 4.91442649501
Circumradius: R = 11.07698142148

Vertex coordinates: A[22; 0] B[0; 0] C[10.25; 12.28656623753]
Centroid: CG[10.75; 4.09552207918]
Coordinates of the circumscribed circle: U[11; 1.24112843145]
Coordinates of the inscribed circle: I[10.5; 4.91442649501]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 133.7233309005° = 133°43'24″ = 0.80876806248 rad
∠ B' = β' = 129.8388439977° = 129°50'18″ = 0.87554843803 rad
∠ C' = γ' = 96.43882510177° = 96°26'18″ = 1.45884276485 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 = 16 ; ; b = 17 ; ; c = 22 ; ;

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

p = a+b+c = 16+17+22 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-16)(27.5-17)(27.5-22) } ; ; T = sqrt{ 18263.44 } = 135.14 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 135.14 }{ 16 } = 16.89 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 135.14 }{ 17 } = 15.9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 135.14 }{ 22 } = 12.29 ; ;

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{ 16**2-17**2-22**2 }{ 2 * 17 * 22 } ) = 46° 16'36" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-16**2-22**2 }{ 2 * 16 * 22 } ) = 50° 9'42" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-16**2-17**2 }{ 2 * 17 * 16 } ) = 83° 33'42" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 135.14 }{ 27.5 } = 4.91 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 46° 16'36" } = 11.07 ; ;




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