22 22 24 triangle

Acute isosceles triangle.

Sides: a = 22   b = 22   c = 24

Area: T = 221.2699066975
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 56.94442688491° = 56°56'39″ = 0.99438649816 rad
Angle ∠ B = β = 56.94442688491° = 56°56'39″ = 0.99438649816 rad
Angle ∠ C = γ = 66.11114623017° = 66°6'41″ = 1.15438626905 rad

Height: ha = 20.1155369725
Height: hb = 20.1155369725
Height: hc = 18.43990889146

Median: ma = 20.22437484162
Median: mb = 20.22437484162
Median: mc = 18.43990889146

Inradius: r = 6.50879137346
Circumradius: R = 13.1244292698

Vertex coordinates: A[24; 0] B[0; 0] C[12; 18.43990889146]
Centroid: CG[12; 6.14663629715]
Coordinates of the circumscribed circle: U[12; 5.31547962166]
Coordinates of the inscribed circle: I[12; 6.50879137346]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 123.0565731151° = 123°3'21″ = 0.99438649816 rad
∠ B' = β' = 123.0565731151° = 123°3'21″ = 0.99438649816 rad
∠ C' = γ' = 113.8898537698° = 113°53'19″ = 1.15438626905 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 = 22 ; ; b = 22 ; ; c = 24 ; ;

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

p = a+b+c = 22+22+24 = 68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 68 }{ 2 } = 34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34 * (34-22)(34-22)(34-24) } ; ; T = sqrt{ 48960 } = 221.27 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 221.27 }{ 22 } = 20.12 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 221.27 }{ 22 } = 20.12 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 221.27 }{ 24 } = 18.44 ; ;

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{ 22**2-22**2-24**2 }{ 2 * 22 * 24 } ) = 56° 56'39" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-22**2-24**2 }{ 2 * 22 * 24 } ) = 56° 56'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-22**2-22**2 }{ 2 * 22 * 22 } ) = 66° 6'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 221.27 }{ 34 } = 6.51 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22 }{ 2 * sin 56° 56'39" } = 13.12 ; ;




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