10 16 22 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 16   c = 22

Area: T = 73.32112111193
Perimeter: p = 48
Semiperimeter: s = 24

Angle ∠ A = α = 24.62199773287° = 24°37'12″ = 0.43296996662 rad
Angle ∠ B = β = 41.80218441931° = 41°48'7″ = 0.73295798146 rad
Angle ∠ C = γ = 113.5788178478° = 113°34'41″ = 1.98223131729 rad

Height: ha = 14.66442422239
Height: hb = 9.16551513899
Height: hc = 6.66655646472

Median: ma = 18.5744175621
Median: mb = 15.10996688705
Median: mc = 7.55498344353

Inradius: r = 3.05550504633
Circumradius: R = 12.0021983963

Vertex coordinates: A[22; 0] B[0; 0] C[7.45545454545; 6.66655646472]
Centroid: CG[9.81881818182; 2.22218548824]
Coordinates of the circumscribed circle: U[11; -4.80107935852]
Coordinates of the inscribed circle: I[8; 3.05550504633]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.3880022671° = 155°22'48″ = 0.43296996662 rad
∠ B' = β' = 138.1988155807° = 138°11'53″ = 0.73295798146 rad
∠ C' = γ' = 66.42218215218° = 66°25'19″ = 1.98223131729 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 = 10 ; ; b = 16 ; ; c = 22 ; ;

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

p = a+b+c = 10+16+22 = 48 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 48 }{ 2 } = 24 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24 * (24-10)(24-16)(24-22) } ; ; T = sqrt{ 5376 } = 73.32 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 73.32 }{ 10 } = 14.66 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 73.32 }{ 16 } = 9.17 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 73.32 }{ 22 } = 6.67 ; ;

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{ 10**2-16**2-22**2 }{ 2 * 16 * 22 } ) = 24° 37'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-10**2-22**2 }{ 2 * 10 * 22 } ) = 41° 48'7" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-10**2-16**2 }{ 2 * 16 * 10 } ) = 113° 34'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 73.32 }{ 24 } = 3.06 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 24° 37'12" } = 12 ; ;




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