5 18 18 triangle

Acute isosceles triangle.

Sides: a = 5   b = 18   c = 18

Area: T = 44.56438586749
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 15.96771122911° = 15°58'2″ = 0.27986786815 rad
Angle ∠ B = β = 82.01664438544° = 82°59″ = 1.4311456986 rad
Angle ∠ C = γ = 82.01664438544° = 82°59″ = 1.4311456986 rad

Height: ha = 17.826554347
Height: hb = 4.95215398528
Height: hc = 4.95215398528

Median: ma = 17.826554347
Median: mb = 9.67695398029
Median: mc = 9.67695398029

Inradius: r = 2.17438467646
Circumradius: R = 9.08880819579

Vertex coordinates: A[18; 0] B[0; 0] C[0.69444444444; 4.95215398528]
Centroid: CG[6.23114814815; 1.65105132843]
Coordinates of the circumscribed circle: U[9; 1.26222336053]
Coordinates of the inscribed circle: I[2.5; 2.17438467646]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.0332887709° = 164°1'58″ = 0.27986786815 rad
∠ B' = β' = 97.98435561456° = 97°59'1″ = 1.4311456986 rad
∠ C' = γ' = 97.98435561456° = 97°59'1″ = 1.4311456986 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 = 5 ; ; b = 18 ; ; c = 18 ; ;

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

p = a+b+c = 5+18+18 = 41 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 41 }{ 2 } = 20.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.5 * (20.5-5)(20.5-18)(20.5-18) } ; ; T = sqrt{ 1985.94 } = 44.56 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 44.56 }{ 5 } = 17.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 44.56 }{ 18 } = 4.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 44.56 }{ 18 } = 4.95 ; ;

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{ 5**2-18**2-18**2 }{ 2 * 18 * 18 } ) = 15° 58'2" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-5**2-18**2 }{ 2 * 5 * 18 } ) = 82° 59" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-5**2-18**2 }{ 2 * 18 * 5 } ) = 82° 59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 44.56 }{ 20.5 } = 2.17 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 15° 58'2" } = 9.09 ; ;




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