22 22 25 triangle

Acute isosceles triangle.

Sides: a = 22   b = 22   c = 25

Area: T = 226.2988337378
Perimeter: p = 69
Semiperimeter: s = 34.5

Angle ∠ A = α = 55.37664645208° = 55°22'35″ = 0.9676501634 rad
Angle ∠ B = β = 55.37664645208° = 55°22'35″ = 0.9676501634 rad
Angle ∠ C = γ = 69.24770709584° = 69°14'49″ = 1.20985893856 rad

Height: ha = 20.57325761253
Height: hb = 20.57325761253
Height: hc = 18.10438669902

Median: ma = 20.82106628137
Median: mb = 20.82106628137
Median: mc = 18.10438669902

Inradius: r = 6.55993720979
Circumradius: R = 13.36773098753

Vertex coordinates: A[25; 0] B[0; 0] C[12.5; 18.10438669902]
Centroid: CG[12.5; 6.03546223301]
Coordinates of the circumscribed circle: U[12.5; 4.73765571149]
Coordinates of the inscribed circle: I[12.5; 6.55993720979]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 124.6243535479° = 124°37'25″ = 0.9676501634 rad
∠ B' = β' = 124.6243535479° = 124°37'25″ = 0.9676501634 rad
∠ C' = γ' = 110.7532929042° = 110°45'11″ = 1.20985893856 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 = 25 ; ;

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

p = a+b+c = 22+22+25 = 69 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 69 }{ 2 } = 34.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34.5 * (34.5-22)(34.5-22)(34.5-25) } ; ; T = sqrt{ 51210.94 } = 226.3 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 226.3 }{ 22 } = 20.57 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 226.3 }{ 22 } = 20.57 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 226.3 }{ 25 } = 18.1 ; ;

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**2-25**2 }{ 2 * 22 * 25 } ) = 55° 22'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-22**2-25**2 }{ 2 * 22 * 25 } ) = 55° 22'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-22**2-22**2 }{ 2 * 22 * 22 } ) = 69° 14'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 226.3 }{ 34.5 } = 6.56 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22 }{ 2 * sin 55° 22'35" } = 13.37 ; ;




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