1 22 22 triangle

Acute isosceles triangle.

Sides: a = 1   b = 22   c = 22

Area: T = 10.9977158724
Perimeter: p = 45
Semiperimeter: s = 22.5

Angle ∠ A = α = 2.60545778704° = 2°36'16″ = 0.04554584595 rad
Angle ∠ B = β = 88.69877110648° = 88°41'52″ = 1.54880670971 rad
Angle ∠ C = γ = 88.69877110648° = 88°41'52″ = 1.54880670971 rad

Height: ha = 21.99443174479
Height: hb = 10.9997417022
Height: hc = 10.9997417022

Median: ma = 21.99443174479
Median: mb = 11.02327038425
Median: mc = 11.02327038425

Inradius: r = 0.489876261
Circumradius: R = 11.00328420101

Vertex coordinates: A[22; 0] B[0; 0] C[0.02327272727; 10.9997417022]
Centroid: CG[7.34109090909; 0.33332472341]
Coordinates of the circumscribed circle: U[11; 0.25500645911]
Coordinates of the inscribed circle: I[0.5; 0.489876261]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 177.395542213° = 177°23'44″ = 0.04554584595 rad
∠ B' = β' = 91.30222889352° = 91°18'8″ = 1.54880670971 rad
∠ C' = γ' = 91.30222889352° = 91°18'8″ = 1.54880670971 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 = 1 ; ; b = 22 ; ; c = 22 ; ;

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

p = a+b+c = 1+22+22 = 45 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 45 }{ 2 } = 22.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22.5 * (22.5-1)(22.5-22)(22.5-22) } ; ; T = sqrt{ 120.94 } = 11 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 11 }{ 1 } = 21.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 11 }{ 22 } = 1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 11 }{ 22 } = 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{ 1**2-22**2-22**2 }{ 2 * 22 * 22 } ) = 2° 36'16" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-1**2-22**2 }{ 2 * 1 * 22 } ) = 88° 41'52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-1**2-22**2 }{ 2 * 22 * 1 } ) = 88° 41'52" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 11 }{ 22.5 } = 0.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1 }{ 2 * sin 2° 36'16" } = 11 ; ;




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