4 18 18 triangle

Acute isosceles triangle.

Sides: a = 4   b = 18   c = 18

Area: T = 35.777708764
Perimeter: p = 40
Semiperimeter: s = 20

Angle ∠ A = α = 12.75987404169° = 12°45'31″ = 0.22326820287 rad
Angle ∠ B = β = 83.62106297916° = 83°37'14″ = 1.45994553125 rad
Angle ∠ C = γ = 83.62106297916° = 83°37'14″ = 1.45994553125 rad

Height: ha = 17.889854382
Height: hb = 3.975523196
Height: hc = 3.975523196

Median: ma = 17.889854382
Median: mb = 9.43439811321
Median: mc = 9.43439811321

Inradius: r = 1.7898854382
Circumradius: R = 9.05660753089

Vertex coordinates: A[18; 0] B[0; 0] C[0.44444444444; 3.975523196]
Centroid: CG[6.14881481481; 1.325507732]
Coordinates of the circumscribed circle: U[9; 1.00662305899]
Coordinates of the inscribed circle: I[2; 1.7898854382]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.2411259583° = 167°14'29″ = 0.22326820287 rad
∠ B' = β' = 96.37993702084° = 96°22'46″ = 1.45994553125 rad
∠ C' = γ' = 96.37993702084° = 96°22'46″ = 1.45994553125 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 = 4 ; ; b = 18 ; ; c = 18 ; ;

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

p = a+b+c = 4+18+18 = 40 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 40 }{ 2 } = 20 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20 * (20-4)(20-18)(20-18) } ; ; T = sqrt{ 1280 } = 35.78 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 35.78 }{ 4 } = 17.89 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 35.78 }{ 18 } = 3.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 35.78 }{ 18 } = 3.98 ; ;

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{ 4**2-18**2-18**2 }{ 2 * 18 * 18 } ) = 12° 45'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-4**2-18**2 }{ 2 * 4 * 18 } ) = 83° 37'14" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-4**2-18**2 }{ 2 * 18 * 4 } ) = 83° 37'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 35.78 }{ 20 } = 1.79 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 12° 45'31" } = 9.06 ; ;




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