5 18 20 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 18   c = 20

Area: T = 43.15659671424
Perimeter: p = 43
Semiperimeter: s = 21.5

Angle ∠ A = α = 13.8722102735° = 13°52'20″ = 0.24221138669 rad
Angle ∠ B = β = 59.66986476367° = 59°40'7″ = 1.04114143615 rad
Angle ∠ C = γ = 106.4599249628° = 106°27'33″ = 1.85880644252 rad

Height: ha = 17.2622386857
Height: hb = 4.79551074603
Height: hc = 4.31655967142

Median: ma = 18.86113361139
Median: mb = 11.46773449412
Median: mc = 8.63113382508

Inradius: r = 2.00772542857
Circumradius: R = 10.42772949906

Vertex coordinates: A[20; 0] B[0; 0] C[2.525; 4.31655967142]
Centroid: CG[7.50883333333; 1.43985322381]
Coordinates of the circumscribed circle: U[10; -2.95444002473]
Coordinates of the inscribed circle: I[3.5; 2.00772542857]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.1287897265° = 166°7'40″ = 0.24221138669 rad
∠ B' = β' = 120.3311352363° = 120°19'53″ = 1.04114143615 rad
∠ C' = γ' = 73.54107503717° = 73°32'27″ = 1.85880644252 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 = 20 ; ;

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

p = a+b+c = 5+18+20 = 43 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 43 }{ 2 } = 21.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21.5 * (21.5-5)(21.5-18)(21.5-20) } ; ; T = sqrt{ 1862.44 } = 43.16 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 43.16 }{ 5 } = 17.26 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 43.16 }{ 18 } = 4.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 43.16 }{ 20 } = 4.32 ; ;

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**2-20**2 }{ 2 * 18 * 20 } ) = 13° 52'20" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-5**2-20**2 }{ 2 * 5 * 20 } ) = 59° 40'7" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-5**2-18**2 }{ 2 * 18 * 5 } ) = 106° 27'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 43.16 }{ 21.5 } = 2.01 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 13° 52'20" } = 10.43 ; ;




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