18 18 22 triangle

Acute isosceles triangle.

Sides: a = 18   b = 18   c = 22

Area: T = 156.7265875336
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 52.33301130357° = 52°19'48″ = 0.91333327704 rad
Angle ∠ B = β = 52.33301130357° = 52°19'48″ = 0.91333327704 rad
Angle ∠ C = γ = 75.34397739287° = 75°20'23″ = 1.31549271128 rad

Height: ha = 17.41439861485
Height: hb = 17.41439861485
Height: hc = 14.24878068488

Median: ma = 17.97222007556
Median: mb = 17.97222007556
Median: mc = 14.24878068488

Inradius: r = 5.40443405288
Circumradius: R = 11.37701709828

Vertex coordinates: A[22; 0] B[0; 0] C[11; 14.24878068488]
Centroid: CG[11; 4.74992689496]
Coordinates of the circumscribed circle: U[11; 2.8787635866]
Coordinates of the inscribed circle: I[11; 5.40443405288]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 127.6769886964° = 127°40'12″ = 0.91333327704 rad
∠ B' = β' = 127.6769886964° = 127°40'12″ = 0.91333327704 rad
∠ C' = γ' = 104.6660226071° = 104°39'37″ = 1.31549271128 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 = 18 ; ; c = 22 ; ;

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

p = a+b+c = 18+18+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 * (29-18)(29-18)(29-22) } ; ; T = sqrt{ 24563 } = 156.73 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 156.73 }{ 18 } = 17.41 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 156.73 }{ 18 } = 17.41 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 156.73 }{ 22 } = 14.25 ; ;

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**2-18**2-22**2 }{ 2 * 18 * 22 } ) = 52° 19'48" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-18**2-22**2 }{ 2 * 18 * 22 } ) = 52° 19'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-18**2-18**2 }{ 2 * 18 * 18 } ) = 75° 20'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 156.73 }{ 29 } = 5.4 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 52° 19'48" } = 11.37 ; ;




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