18 20 20 triangle

Acute isosceles triangle.

Sides: a = 18   b = 20   c = 20

Area: T = 160.7455139895
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 53.48773679008° = 53°29'15″ = 0.93435306781 rad
Angle ∠ B = β = 63.25663160496° = 63°15'23″ = 1.10440309877 rad
Angle ∠ C = γ = 63.25663160496° = 63°15'23″ = 1.10440309877 rad

Height: ha = 17.86105710995
Height: hb = 16.07545139895
Height: hc = 16.07545139895

Median: ma = 17.86105710995
Median: mb = 16.18664140562
Median: mc = 16.18664140562

Inradius: r = 5.54329358585
Circumradius: R = 11.19878502191

Vertex coordinates: A[20; 0] B[0; 0] C[8.1; 16.07545139895]
Centroid: CG[9.36766666667; 5.35881713298]
Coordinates of the circumscribed circle: U[10; 5.03990325986]
Coordinates of the inscribed circle: I[9; 5.54329358585]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 126.5132632099° = 126°30'45″ = 0.93435306781 rad
∠ B' = β' = 116.744368395° = 116°44'37″ = 1.10440309877 rad
∠ C' = γ' = 116.744368395° = 116°44'37″ = 1.10440309877 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 = 20 ; ; c = 20 ; ;

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

p = a+b+c = 18+20+20 = 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)(29-20)(29-20) } ; ; T = sqrt{ 25839 } = 160.75 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 160.75 }{ 18 } = 17.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 160.75 }{ 20 } = 16.07 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 160.75 }{ 20 } = 16.07 ; ;

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**2-20**2-20**2 }{ 2 * 20 * 20 } ) = 53° 29'15" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-18**2-20**2 }{ 2 * 18 * 20 } ) = 63° 15'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-18**2-20**2 }{ 2 * 20 * 18 } ) = 63° 15'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 160.75 }{ 29 } = 5.54 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 53° 29'15" } = 11.2 ; ;




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