5 15 18 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 15   c = 18

Area: T = 32.61990128606
Perimeter: p = 38
Semiperimeter: s = 19

Angle ∠ A = α = 13.98223106495° = 13°58'56″ = 0.24440373579 rad
Angle ∠ B = β = 46.45877809718° = 46°27'28″ = 0.81108412411 rad
Angle ∠ C = γ = 119.5659908379° = 119°33'36″ = 2.08767140546 rad

Height: ha = 13.04876051442
Height: hb = 4.34992017147
Height: hc = 3.62443347623

Median: ma = 16.37883393542
Median: mb = 10.87442815855
Median: mc = 6.63332495807

Inradius: r = 1.71767901506
Circumradius: R = 10.34767263538

Vertex coordinates: A[18; 0] B[0; 0] C[3.44444444444; 3.62443347623]
Centroid: CG[7.14881481481; 1.20881115874]
Coordinates of the circumscribed circle: U[9; -5.10443850012]
Coordinates of the inscribed circle: I[4; 1.71767901506]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.0187689351° = 166°1'4″ = 0.24440373579 rad
∠ B' = β' = 133.5422219028° = 133°32'32″ = 0.81108412411 rad
∠ C' = γ' = 60.44400916213° = 60°26'24″ = 2.08767140546 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 = 15 ; ; c = 18 ; ;

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

p = a+b+c = 5+15+18 = 38 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 38 }{ 2 } = 19 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19 * (19-5)(19-15)(19-18) } ; ; T = sqrt{ 1064 } = 32.62 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 32.62 }{ 5 } = 13.05 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 32.62 }{ 15 } = 4.35 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 32.62 }{ 18 } = 3.62 ; ;

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**2-15**2-18**2 }{ 2 * 15 * 18 } ) = 13° 58'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-5**2-18**2 }{ 2 * 5 * 18 } ) = 46° 27'28" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-5**2-15**2 }{ 2 * 15 * 5 } ) = 119° 33'36" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 32.62 }{ 19 } = 1.72 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 13° 58'56" } = 10.35 ; ;




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