22 24 24 triangle

Acute isosceles triangle.

Sides: a = 22   b = 24   c = 24

Area: T = 234.6388019085
Perimeter: p = 70
Semiperimeter: s = 35

Angle ∠ A = α = 54.5599225472° = 54°33'33″ = 0.95222381218 rad
Angle ∠ B = β = 62.7220387264° = 62°43'13″ = 1.09546772659 rad
Angle ∠ C = γ = 62.7220387264° = 62°43'13″ = 1.09546772659 rad

Height: ha = 21.33107290077
Height: hb = 19.55331682571
Height: hc = 19.55331682571

Median: ma = 21.33107290077
Median: mb = 19.64768827044
Median: mc = 19.64768827044

Inradius: r = 6.70439434024
Circumradius: R = 13.5021648251

Vertex coordinates: A[24; 0] B[0; 0] C[10.08333333333; 19.55331682571]
Centroid: CG[11.36111111111; 6.51877227524]
Coordinates of the circumscribed circle: U[12; 6.18882554484]
Coordinates of the inscribed circle: I[11; 6.70439434024]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.4410774528° = 125°26'27″ = 0.95222381218 rad
∠ B' = β' = 117.2879612736° = 117°16'47″ = 1.09546772659 rad
∠ C' = γ' = 117.2879612736° = 117°16'47″ = 1.09546772659 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 = 24 ; ; c = 24 ; ;

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

p = a+b+c = 22+24+24 = 70 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 70 }{ 2 } = 35 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35 * (35-22)(35-24)(35-24) } ; ; T = sqrt{ 55055 } = 234.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 234.64 }{ 22 } = 21.33 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 234.64 }{ 24 } = 19.55 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 234.64 }{ 24 } = 19.55 ; ;

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**2-24**2-24**2 }{ 2 * 24 * 24 } ) = 54° 33'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-22**2-24**2 }{ 2 * 22 * 24 } ) = 62° 43'13" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-22**2-24**2 }{ 2 * 24 * 22 } ) = 62° 43'13" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 234.64 }{ 35 } = 6.7 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22 }{ 2 * sin 54° 33'33" } = 13.5 ; ;




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