13 18 18 triangle

Acute isosceles triangle.

Sides: a = 13   b = 18   c = 18

Area: T = 109.1055167155
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 42.33768976917° = 42°20'13″ = 0.73989182598 rad
Angle ∠ B = β = 68.83215511542° = 68°49'54″ = 1.20113371969 rad
Angle ∠ C = γ = 68.83215511542° = 68°49'54″ = 1.20113371969 rad

Height: ha = 16.78554103316
Height: hb = 12.12327963506
Height: hc = 12.12327963506

Median: ma = 16.78554103316
Median: mb = 12.86546803303
Median: mc = 12.86546803303

Inradius: r = 4.45332721288
Circumradius: R = 9.65112385935

Vertex coordinates: A[18; 0] B[0; 0] C[4.69444444444; 12.12327963506]
Centroid: CG[7.56548148148; 4.04109321169]
Coordinates of the circumscribed circle: U[9; 3.48551694921]
Coordinates of the inscribed circle: I[6.5; 4.45332721288]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.6633102308° = 137°39'47″ = 0.73989182598 rad
∠ B' = β' = 111.1688448846° = 111°10'6″ = 1.20113371969 rad
∠ C' = γ' = 111.1688448846° = 111°10'6″ = 1.20113371969 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 = 13 ; ; b = 18 ; ; c = 18 ; ;

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

p = a+b+c = 13+18+18 = 49 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 49 }{ 2 } = 24.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24.5 * (24.5-13)(24.5-18)(24.5-18) } ; ; T = sqrt{ 11903.94 } = 109.11 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 109.11 }{ 13 } = 16.79 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 109.11 }{ 18 } = 12.12 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 109.11 }{ 18 } = 12.12 ; ;

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{ 13**2-18**2-18**2 }{ 2 * 18 * 18 } ) = 42° 20'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-13**2-18**2 }{ 2 * 13 * 18 } ) = 68° 49'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-13**2-18**2 }{ 2 * 18 * 13 } ) = 68° 49'54" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 109.11 }{ 24.5 } = 4.45 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 42° 20'13" } = 9.65 ; ;




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