14 22 22 triangle

Acute isosceles triangle.

Sides: a = 14   b = 22   c = 22

Area: T = 145.9976575302
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 37.106600907° = 37°6'22″ = 0.64876220305 rad
Angle ∠ B = β = 71.4476995465° = 71°26'49″ = 1.24769853115 rad
Angle ∠ C = γ = 71.4476995465° = 71°26'49″ = 1.24769853115 rad

Height: ha = 20.85766536146
Height: hb = 13.27224159366
Height: hc = 13.27224159366

Median: ma = 20.85766536146
Median: mb = 14.79986485869
Median: mc = 14.79986485869

Inradius: r = 5.03443646656
Circumradius: R = 11.60330118959

Vertex coordinates: A[22; 0] B[0; 0] C[4.45545454545; 13.27224159366]
Centroid: CG[8.81881818182; 4.42441386455]
Coordinates of the circumscribed circle: U[11; 3.69218674214]
Coordinates of the inscribed circle: I[7; 5.03443646656]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.894399093° = 142°53'38″ = 0.64876220305 rad
∠ B' = β' = 108.5533004535° = 108°33'11″ = 1.24769853115 rad
∠ C' = γ' = 108.5533004535° = 108°33'11″ = 1.24769853115 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 = 14 ; ; b = 22 ; ; c = 22 ; ;

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

p = a+b+c = 14+22+22 = 58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 58 }{ 2 } = 29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29 * (29-14)(29-22)(29-22) } ; ; T = sqrt{ 21315 } = 146 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 146 }{ 14 } = 20.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 146 }{ 22 } = 13.27 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 146 }{ 22 } = 13.27 ; ;

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{ 14**2-22**2-22**2 }{ 2 * 22 * 22 } ) = 37° 6'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-14**2-22**2 }{ 2 * 14 * 22 } ) = 71° 26'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-14**2-22**2 }{ 2 * 22 * 14 } ) = 71° 26'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 146 }{ 29 } = 5.03 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 37° 6'22" } = 11.6 ; ;




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