9 17 18 triangle

Acute scalene triangle.

Sides: a = 9   b = 17   c = 18

Area: T = 75.63106816048
Perimeter: p = 44
Semiperimeter: s = 22

Angle ∠ A = α = 29.62548004283° = 29°37'29″ = 0.51770503077 rad
Angle ∠ B = β = 69.02110649855° = 69°1'16″ = 1.20546448372 rad
Angle ∠ C = γ = 81.35441345862° = 81°21'15″ = 1.42198975086 rad

Height: ha = 16.80768181344
Height: hb = 8.89877272476
Height: hc = 8.40334090672

Median: ma = 16.91989243157
Median: mb = 11.41327122105
Median: mc = 10.19880390272

Inradius: r = 3.43877582548
Circumradius: R = 9.10334483016

Vertex coordinates: A[18; 0] B[0; 0] C[3.22222222222; 8.40334090672]
Centroid: CG[7.07440740741; 2.80111363557]
Coordinates of the circumscribed circle: U[9; 1.36884922283]
Coordinates of the inscribed circle: I[5; 3.43877582548]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.3755199572° = 150°22'31″ = 0.51770503077 rad
∠ B' = β' = 110.9798935015° = 110°58'44″ = 1.20546448372 rad
∠ C' = γ' = 98.64658654138° = 98°38'45″ = 1.42198975086 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 = 9 ; ; b = 17 ; ; c = 18 ; ;

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

p = a+b+c = 9+17+18 = 44 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 44 }{ 2 } = 22 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22 * (22-9)(22-17)(22-18) } ; ; T = sqrt{ 5720 } = 75.63 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 75.63 }{ 9 } = 16.81 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 75.63 }{ 17 } = 8.9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 75.63 }{ 18 } = 8.4 ; ;

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{ 9**2-17**2-18**2 }{ 2 * 17 * 18 } ) = 29° 37'29" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-9**2-18**2 }{ 2 * 9 * 18 } ) = 69° 1'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-9**2-17**2 }{ 2 * 17 * 9 } ) = 81° 21'15" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 75.63 }{ 22 } = 3.44 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 29° 37'29" } = 9.1 ; ;




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