18 22 22 triangle

Acute isosceles triangle.

Sides: a = 18   b = 22   c = 22

Area: T = 180.6743739099
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 48.2955479834° = 48°17'44″ = 0.84329151369 rad
Angle ∠ B = β = 65.8522260083° = 65°51'8″ = 1.14993387583 rad
Angle ∠ C = γ = 65.8522260083° = 65°51'8″ = 1.14993387583 rad

Height: ha = 20.07548598999
Height: hb = 16.42548853726
Height: hc = 16.42548853726

Median: ma = 20.07548598999
Median: mb = 16.82326038413
Median: mc = 16.82326038413

Inradius: r = 5.82881851322
Circumradius: R = 12.05548786496

Vertex coordinates: A[22; 0] B[0; 0] C[7.36436363636; 16.42548853726]
Centroid: CG[9.78878787879; 5.47549617909]
Coordinates of the circumscribed circle: U[11; 4.93215412657]
Coordinates of the inscribed circle: I[9; 5.82881851322]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131.7054520166° = 131°42'16″ = 0.84329151369 rad
∠ B' = β' = 114.1487739917° = 114°8'52″ = 1.14993387583 rad
∠ C' = γ' = 114.1487739917° = 114°8'52″ = 1.14993387583 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 = 18 ; ; b = 22 ; ; c = 22 ; ;

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

p = a+b+c = 18+22+22 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-18)(31-22)(31-22) } ; ; T = sqrt{ 32643 } = 180.67 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 180.67 }{ 18 } = 20.07 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 180.67 }{ 22 } = 16.42 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 180.67 }{ 22 } = 16.42 ; ;

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{ 18**2-22**2-22**2 }{ 2 * 22 * 22 } ) = 48° 17'44" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-18**2-22**2 }{ 2 * 18 * 22 } ) = 65° 51'8" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-18**2-22**2 }{ 2 * 22 * 18 } ) = 65° 51'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 180.67 }{ 31 } = 5.83 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 48° 17'44" } = 12.05 ; ;




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