16 22 22 triangle

Acute isosceles triangle.

Sides: a = 16   b = 22   c = 22

Area: T = 163.9511212255
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 42.6477372527° = 42°38'51″ = 0.74443370679 rad
Angle ∠ B = β = 68.67663137365° = 68°40'35″ = 1.19986277928 rad
Angle ∠ C = γ = 68.67663137365° = 68°40'35″ = 1.19986277928 rad

Height: ha = 20.49439015319
Height: hb = 14.90546556596
Height: hc = 14.90546556596

Median: ma = 20.49439015319
Median: mb = 15.78797338381
Median: mc = 15.78797338381

Inradius: r = 5.46550404085
Circumradius: R = 11.80883908827

Vertex coordinates: A[22; 0] B[0; 0] C[5.81881818182; 14.90546556596]
Centroid: CG[9.27327272727; 4.96882185532]
Coordinates of the circumscribed circle: U[11; 4.2943960321]
Coordinates of the inscribed circle: I[8; 5.46550404085]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.3532627473° = 137°21'9″ = 0.74443370679 rad
∠ B' = β' = 111.3243686263° = 111°19'25″ = 1.19986277928 rad
∠ C' = γ' = 111.3243686263° = 111°19'25″ = 1.19986277928 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 = 22 ; ; c = 22 ; ;

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

p = a+b+c = 16+22+22 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-16)(30-22)(30-22) } ; ; T = sqrt{ 26880 } = 163.95 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 163.95 }{ 16 } = 20.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 163.95 }{ 22 } = 14.9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 163.95 }{ 22 } = 14.9 ; ;

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**2-22**2-22**2 }{ 2 * 22 * 22 } ) = 42° 38'51" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-16**2-22**2 }{ 2 * 16 * 22 } ) = 68° 40'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-16**2-22**2 }{ 2 * 22 * 16 } ) = 68° 40'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 163.95 }{ 30 } = 5.47 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 42° 38'51" } = 11.81 ; ;




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